LMFDB - Embedded newform 465.2.k.a.218.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [465,2,Mod(32,465)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("465.32"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(465, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([2, 1, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 465 = 3 \cdot 5 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	465.k (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [60,0,0,0,0,-4,0,0,0,-32] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(10)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$3.71304369399$
Analytic rank:	$0$
Dimension:	$60$
Relative dimension:	$30$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			218.2
Character	$\chi$	$=$	465.218
Dual form			465.2.k.a.32.2

$q$-expansion

comment:q-expansion

sage:f.q_expansion() # note that sage often uses an isomorphic number field

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.93363 - 1.93363i) q^{2} +(-1.43955 + 0.963170i) q^{3} +5.47785i q^{4} +(-1.96536 - 1.06648i) q^{5} +(4.64597 + 0.921141i) q^{6} +(1.12676 - 1.12676i) q^{7} +(6.72487 - 6.72487i) q^{8} +(1.14461 - 2.77306i) q^{9} +(1.73810 + 5.86244i) q^{10} +0.704412i q^{11} +(-5.27610 - 7.88564i) q^{12} +(-4.82163 - 4.82163i) q^{13} -4.35746 q^{14} +(3.85643 - 0.357727i) q^{15} -15.0511 q^{16} +(1.83808 + 1.83808i) q^{17} +(-7.57532 + 3.14883i) q^{18} +1.74662i q^{19} +(5.84200 - 10.7659i) q^{20} +(-0.536764 + 2.70728i) q^{21} +(1.36207 - 1.36207i) q^{22} +(2.24021 - 2.24021i) q^{23} +(-3.20359 + 16.1580i) q^{24} +(2.72526 + 4.19201i) q^{25} +18.6465i q^{26} +(1.02321 + 5.09441i) q^{27} +(6.17221 + 6.17221i) q^{28} -4.83228 q^{29} +(-8.14862 - 6.76519i) q^{30} +1.00000 q^{31} +(15.6536 + 15.6536i) q^{32} +(-0.678468 - 1.01404i) q^{33} -7.10835i q^{34} +(-3.41614 + 1.01282i) q^{35} +(15.1904 + 6.26998i) q^{36} +(-6.24498 + 6.24498i) q^{37} +(3.37732 - 3.37732i) q^{38} +(11.5850 + 2.29692i) q^{39} +(-20.3887 + 6.04486i) q^{40} +5.49292i q^{41} +(6.27278 - 4.19698i) q^{42} +(0.999538 + 0.999538i) q^{43} -3.85866 q^{44} +(-5.20697 + 4.22936i) q^{45} -8.66347 q^{46} +(-5.28289 - 5.28289i) q^{47} +(21.6669 - 14.4968i) q^{48} +4.46084i q^{49} +(2.83617 - 13.3754i) q^{50} +(-4.41640 - 0.875625i) q^{51} +(26.4122 - 26.4122i) q^{52} +(-2.76712 + 2.76712i) q^{53} +(7.87219 - 11.8292i) q^{54} +(0.751239 - 1.38442i) q^{55} -15.1546i q^{56} +(-1.68230 - 2.51435i) q^{57} +(9.34383 + 9.34383i) q^{58} +1.42235 q^{59} +(1.95958 + 21.1249i) q^{60} +4.88455 q^{61} +(-1.93363 - 1.93363i) q^{62} +(-1.83488 - 4.41426i) q^{63} -30.4342i q^{64} +(4.33407 + 14.6184i) q^{65} +(-0.648863 + 3.27268i) q^{66} +(-6.87690 + 6.87690i) q^{67} +(-10.0687 + 10.0687i) q^{68} +(-1.06719 + 5.38260i) q^{69} +(8.56397 + 4.64713i) q^{70} +14.6338i q^{71} +(-10.9512 - 26.3458i) q^{72} +(5.99532 + 5.99532i) q^{73} +24.1510 q^{74} +(-7.96076 - 3.40973i) q^{75} -9.56774 q^{76} +(0.793701 + 0.793701i) q^{77} +(-17.9597 - 26.8425i) q^{78} -11.7893i q^{79} +(29.5809 + 16.0517i) q^{80} +(-6.37975 - 6.34813i) q^{81} +(10.6213 - 10.6213i) q^{82} +(-8.42829 + 8.42829i) q^{83} +(-14.8301 - 2.94031i) q^{84} +(-1.65222 - 5.57276i) q^{85} -3.86547i q^{86} +(6.95630 - 4.65430i) q^{87} +(4.73708 + 4.73708i) q^{88} -12.0272 q^{89} +(18.2464 + 1.89032i) q^{90} -10.8656 q^{91} +(12.2715 + 12.2715i) q^{92} +(-1.43955 + 0.963170i) q^{93} +20.4303i q^{94} +(1.86273 - 3.43274i) q^{95} +(-37.6112 - 7.45704i) q^{96} +(0.0249208 - 0.0249208i) q^{97} +(8.62561 - 8.62561i) q^{98} +(1.95338 + 0.806274i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 60 q - 4 q^{6} - 32 q^{10} + 4 q^{13} + 20 q^{15} - 60 q^{16} - 46 q^{18} - 4 q^{21} + 8 q^{22} - 8 q^{25} - 6 q^{27} + 112 q^{28} + 54 q^{30} + 60 q^{31} - 30 q^{33} - 4 q^{36} - 36 q^{37} - 36 q^{40}+ \cdots - 8 q^{97}+O(q^{100}) $ 60 * q - 4 * q^6 - 32 * q^10 + 4 * q^13 + 20 * q^15 - 60 * q^16 - 46 * q^18 - 4 * q^21 + 8 * q^22 - 8 * q^25 - 6 * q^27 + 112 * q^28 + 54 * q^30 + 60 * q^31 - 30 * q^33 - 4 * q^36 - 36 * q^37 - 36 * q^40 + 44 * q^42 + 16 * q^43 + 14 * q^45 + 40 * q^46 - 104 * q^48 - 48 * q^51 - 12 * q^52 - 48 * q^55 + 42 * q^57 + 80 * q^58 + 60 * q^60 - 8 * q^61 - 10 * q^63 - 24 * q^66 - 88 * q^67 - 84 * q^70 + 84 * q^72 + 60 * q^73 + 14 * q^75 + 72 * q^76 - 152 * q^78 - 132 * q^81 - 60 * q^82 - 16 * q^85 + 34 * q^87 + 124 * q^88 + 190 * q^90 + 64 * q^91 - 88 * q^96 - 8 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/465\mathbb{Z}\right)^\times$.

$n$	$187$	$311$	$406$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$-1$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−1.93363	−	1.93363i	−1.36728	−	1.36728i	−0.864291	−	0.502992i	$-0.832233\pi$
$2$	−1.93363	−	1.93363i	−1.36728	−	1.36728i	−0.502992	−	0.864291i	$-0.667767\pi$
$3$	−1.43955	+	0.963170i	−0.831124	+	0.556087i
$3$	−1.43955	+	0.963170i	−0.831124	+	0.556087i
$4$			5.47785i			2.73892i
$5$	−1.96536	−	1.06648i	−0.878934	−	0.476943i
$5$	−1.96536	−	1.06648i	−0.878934	−	0.476943i
$6$	4.64597	+	0.921141i	1.89671	+	0.376054i
$7$	1.12676	−	1.12676i	0.425874	−	0.425874i	−0.461346	−	0.887220i	$-0.652633\pi$
$7$	1.12676	−	1.12676i	0.425874	−	0.425874i	0.887220	+	0.461346i	$0.152633\pi$
$8$	6.72487	−	6.72487i	2.37760	−	2.37760i
$9$	1.14461	−	2.77306i	0.381535	−	0.924354i
$10$	1.73810	+	5.86244i	0.549636	+	1.85387i
$11$			0.704412i			0.212388i	0.994345	+	0.106194i	$0.0338665\pi$
$11$			0.704412i			0.212388i	−0.994345	+	0.106194i	$0.966134\pi$
$12$	−5.27610	−	7.88564i	−1.52308	−	2.27639i
$13$	−4.82163	−	4.82163i	−1.33728	−	1.33728i	−0.898685	−	0.438594i	$-0.855477\pi$
$13$	−4.82163	−	4.82163i	−1.33728	−	1.33728i	−0.438594	−	0.898685i	$-0.644523\pi$
$14$	−4.35746			−1.16458
$15$	3.85643	−	0.357727i	0.995725	−	0.0923648i
$16$	−15.0511			−3.76278
$17$	1.83808	+	1.83808i	0.445801	+	0.445801i	0.893956	−	0.448155i	$-0.147919\pi$
$17$	1.83808	+	1.83808i	0.445801	+	0.445801i	−0.448155	+	0.893956i	$0.647919\pi$
$18$	−7.57532	+	3.14883i	−1.78552	+	0.742187i
$19$			1.74662i			0.400703i	0.979724	+	0.200351i	$0.0642084\pi$
$19$			1.74662i			0.400703i	−0.979724	+	0.200351i	$0.935792\pi$
$20$	5.84200	−	10.7659i	1.30631	−	2.40734i
$21$	−0.536764	+	2.70728i	−0.117131	+	0.590777i
$22$	1.36207	−	1.36207i	0.290395	−	0.290395i
$23$	2.24021	−	2.24021i	0.467116	−	0.467116i	−0.433863	−	0.900979i	$-0.642850\pi$
$23$	2.24021	−	2.24021i	0.467116	−	0.467116i	0.900979	+	0.433863i	$0.142850\pi$
$24$	−3.20359	+	16.1580i	−0.653930	+	3.29824i
$25$	2.72526	+	4.19201i	0.545051	+	0.838403i
$26$			18.6465i			3.65688i
$27$	1.02321	+	5.09441i	0.196918	+	0.980420i
$28$	6.17221	+	6.17221i	1.16644	+	1.16644i
$29$	−4.83228			−0.897331			−0.448665	−	0.893700i	$-0.648101\pi$
$29$	−4.83228			−0.897331			−0.448665	+	0.893700i	$0.648101\pi$
$30$	−8.14862	−	6.76519i	−1.48773	−	1.23515i
$31$	1.00000			0.179605
$31$	1.00000			0.179605
$32$	15.6536	+	15.6536i	2.76719	+	2.76719i
$33$	−0.678468	−	1.01404i	−0.118106	−	0.176521i
$34$		−	7.10835i		−	1.21907i
$35$	−3.41614	+	1.01282i	−0.577433	+	0.171198i
$36$	15.1904	+	6.26998i	2.53174	+	1.04500i
$37$	−6.24498	+	6.24498i	−1.02667	+	1.02667i	−0.0270342	+	0.999635i	$0.508606\pi$
$37$	−6.24498	+	6.24498i	−1.02667	+	1.02667i	−0.999635	+	0.0270342i	$0.991394\pi$
$38$	3.37732	−	3.37732i	0.547874	−	0.547874i
$39$	11.5850	+	2.29692i	1.85509	+	0.367802i
$40$	−20.3887	+	6.04486i	−3.22374	+	0.955776i
$41$			5.49292i			0.857851i	0.903340	+	0.428925i	$0.141108\pi$
$41$			5.49292i			0.857851i	−0.903340	+	0.428925i	$0.858892\pi$
$42$	6.27278	−	4.19698i	0.967912	−	0.647608i
$43$	0.999538	+	0.999538i	0.152428	+	0.152428i	0.779202	−	0.626773i	$-0.215625\pi$
$43$	0.999538	+	0.999538i	0.152428	+	0.152428i	−0.626773	+	0.779202i	$0.715625\pi$
$44$	−3.85866			−0.581715
$45$	−5.20697	+	4.22936i	−0.776209	+	0.630476i
$46$	−8.66347			−1.27736
$47$	−5.28289	−	5.28289i	−0.770589	−	0.770589i	0.207620	−	0.978209i	$-0.433428\pi$
$47$	−5.28289	−	5.28289i	−0.770589	−	0.770589i	−0.978209	+	0.207620i	$0.933428\pi$
$48$	21.6669	−	14.4968i	3.12734	−	2.09243i
$49$			4.46084i			0.637262i
$50$	2.83617	−	13.3754i	0.401095	−	1.89157i
$51$	−4.41640	−	0.875625i	−0.618420	−	0.122612i
$52$	26.4122	−	26.4122i	3.66271	−	3.66271i
$53$	−2.76712	+	2.76712i	−0.380094	+	0.380094i	−0.871136	−	0.491042i	$-0.836616\pi$
$53$	−2.76712	+	2.76712i	−0.380094	+	0.380094i	0.491042	+	0.871136i	$0.336616\pi$
$54$	7.87219	−	11.8292i	1.07127	−	1.60975i
$55$	0.751239	−	1.38442i	0.101297	−	0.186675i
$56$		−	15.1546i		−	2.02512i
$57$	−1.68230	−	2.51435i	−0.222825	−	0.333034i
$58$	9.34383	+	9.34383i	1.22691	+	1.22691i
$59$	1.42235			0.185175			0.0925873	−	0.995705i	$-0.470486\pi$
$59$	1.42235			0.185175			0.0925873	+	0.995705i	$0.470486\pi$
$60$	1.95958	+	21.1249i	0.252980	+	2.72722i
$61$	4.88455			0.625402			0.312701	−	0.949852i	$-0.398766\pi$
$61$	4.88455			0.625402			0.312701	+	0.949852i	$0.398766\pi$
$62$	−1.93363	−	1.93363i	−0.245571	−	0.245571i
$63$	−1.83488	−	4.41426i	−0.231173	−	0.556145i
$64$		−	30.4342i		−	3.80428i
$65$	4.33407	+	14.6184i	0.537575	+	1.81319i
$66$	−0.648863	+	3.27268i	−0.0798695	+	0.402839i
$67$	−6.87690	+	6.87690i	−0.840147	+	0.840147i	−0.988878	−	0.148730i	$-0.952481\pi$
$67$	−6.87690	+	6.87690i	−0.840147	+	0.840147i	0.148730	+	0.988878i	$0.452481\pi$
$68$	−10.0687	+	10.0687i	−1.22101	+	1.22101i
$69$	−1.06719	+	5.38260i	−0.128475	+	0.647988i
$70$	8.56397	+	4.64713i	1.02359	+	0.555439i
$71$			14.6338i			1.73671i	0.495941	+	0.868356i	$0.334823\pi$
$71$			14.6338i			1.73671i	−0.495941	+	0.868356i	$0.665177\pi$
$72$	−10.9512	−	26.3458i	−1.29061	−	3.10489i
$73$	5.99532	+	5.99532i	0.701699	+	0.701699i	0.964775	−	0.263076i	$-0.0847369\pi$
$73$	5.99532	+	5.99532i	0.701699	+	0.701699i	−0.263076	+	0.964775i	$0.584737\pi$
$74$	24.1510			2.80749
$75$	−7.96076	−	3.40973i	−0.919230	−	0.393721i
$76$	−9.56774			−1.09749
$77$	0.793701	+	0.793701i	0.0904506	+	0.0904506i
$78$	−17.9597	−	26.8425i	−2.03354	−	3.03932i
$79$		−	11.7893i		−	1.32640i	−0.748442	−	0.663201i	$-0.769198\pi$
$79$		−	11.7893i		−	1.32640i	0.748442	−	0.663201i	$-0.230802\pi$
$80$	29.5809	+	16.0517i	3.30724	+	1.79463i
$81$	−6.37975	−	6.34813i	−0.708862	−	0.705348i
$82$	10.6213	−	10.6213i	1.17292	−	1.17292i
$83$	−8.42829	+	8.42829i	−0.925125	+	0.925125i	−0.997386	−	0.0722611i	$-0.976979\pi$
$83$	−8.42829	+	8.42829i	−0.925125	+	0.925125i	0.0722611	+	0.997386i	$0.476979\pi$
$84$	−14.8301	−	2.94031i	−1.61809	−	0.320814i
$85$	−1.65222	−	5.57276i	−0.179208	−	0.604451i
$86$		−	3.86547i		−	0.416825i
$87$	6.95630	−	4.65430i	0.745794	−	0.498994i
$88$	4.73708	+	4.73708i	0.504975	+	0.504975i
$89$	−12.0272			−1.27488			−0.637438	−	0.770501i	$-0.720006\pi$
$89$	−12.0272			−1.27488			−0.637438	+	0.770501i	$0.720006\pi$
$90$	18.2464	+	1.89032i	1.92334	+	0.199258i
$91$	−10.8656			−1.13903
$92$	12.2715	+	12.2715i	1.27940	+	1.27940i
$93$	−1.43955	+	0.963170i	−0.149274	+	0.0998761i
$94$			20.4303i			2.10723i
$95$	1.86273	−	3.43274i	0.191112	−	0.352191i
$96$	−37.6112	−	7.45704i	−3.83867	−	0.761081i
$97$	0.0249208	−	0.0249208i	0.00253032	−	0.00253032i	−0.705840	−	0.708371i	$-0.749430\pi$
$97$	0.0249208	−	0.0249208i	0.00253032	−	0.00253032i	0.708371	+	0.705840i	$0.249430\pi$
$98$	8.62561	−	8.62561i	0.871318	−	0.871318i
$99$	1.95338	+	0.806274i	0.196322	+	0.0810336i
$100$	−22.9632	+	14.9285i	−2.29632	+	1.49285i
$101$		−	9.87984i		−	0.983081i	−0.870855	−	0.491541i	$-0.836434\pi$
$101$		−	9.87984i		−	0.983081i	0.870855	−	0.491541i	$-0.163566\pi$
$102$	6.84655	+	10.2328i	0.677909	+	1.01320i
$103$	−3.02060	−	3.02060i	−0.297629	−	0.297629i	0.542456	−	0.840085i	$-0.317495\pi$
$103$	−3.02060	−	3.02060i	−0.297629	−	0.297629i	−0.840085	+	0.542456i	$0.817495\pi$
$104$	−64.8497			−6.35904
$105$	3.94219	−	4.74833i	0.384718	−	0.463390i
$106$	10.7012			1.03939
$107$	8.51336	+	8.51336i	0.823018	+	0.823018i	0.986540	−	0.163522i	$-0.0522855\pi$
$107$	8.51336	+	8.51336i	0.823018	+	0.823018i	−0.163522	+	0.986540i	$0.552286\pi$
$108$	−27.9064	+	5.60502i	−2.68530	+	0.539343i
$109$			12.2850i			1.17668i	0.808612	+	0.588342i	$0.200219\pi$
$109$			12.2850i			1.17668i	−0.808612	+	0.588342i	$0.799781\pi$
$110$	−4.12957	+	1.22434i	−0.393739	+	0.116736i
$111$	2.97498	−	15.0049i	0.282373	−	1.42421i
$112$	−16.9590	+	16.9590i	−1.60247	+	1.60247i
$113$	0.541732	−	0.541732i	0.0509619	−	0.0509619i	−0.681167	−	0.732128i	$-0.738527\pi$
$113$	0.541732	−	0.541732i	0.0509619	−	0.0509619i	0.732128	+	0.681167i	$0.238527\pi$
$114$	−1.60889	+	8.11476i	−0.150686	+	0.760017i
$115$	−6.79194	+	2.01368i	−0.633352	+	0.187777i
$116$		−	26.4705i		−	2.45772i
$117$	−18.8895	+	7.85181i	−1.74634	+	0.725900i
$118$	−2.75030	−	2.75030i	−0.253186	−	0.253186i
$119$	4.14215			0.379710
$120$	23.5283	−	28.3397i	2.14783	−	2.58705i
$121$	10.5038			0.954891
$122$	−9.44490	−	9.44490i	−0.855101	−	0.855101i
$123$	−5.29062	−	7.90734i	−0.477039	−	0.712980i
$124$			5.47785i			0.491925i
$125$	−0.885415	−	11.1452i	−0.0791939	−	0.996859i
$126$	−4.98758	+	12.0835i	−0.444329	+	1.07649i
$127$	−15.0880	+	15.0880i	−1.33884	+	1.33884i	−0.441661	+	0.897182i	$0.645611\pi$
$127$	−15.0880	+	15.0880i	−1.33884	+	1.33884i	−0.897182	+	0.441661i	$0.854389\pi$
$128$	−27.5413	+	27.5413i	−2.43433	+	2.43433i
$129$	−2.40161	−	0.476159i	−0.211450	−	0.0419235i
$130$	19.8860	−	36.6470i	1.74412	−	3.21416i
$131$		−	1.42034i		−	0.124096i	−0.998073	−	0.0620480i	$-0.980237\pi$
$131$		−	1.42034i		−	0.124096i	0.998073	−	0.0620480i	$-0.0197632\pi$
$132$	5.55474	−	3.71655i	0.483478	−	0.323484i
$133$	1.96802	+	1.96802i	0.170649	+	0.170649i
$134$	26.5948			2.29744
$135$	3.42209	−	11.1036i	0.294527	−	0.955643i
$136$	24.7218			2.11987
$137$	2.82944	+	2.82944i	0.241736	+	0.241736i	0.817568	−	0.575832i	$-0.195322\pi$
$137$	2.82944	+	2.82944i	0.241736	+	0.241736i	−0.575832	+	0.817568i	$0.695322\pi$
$138$	12.4715	−	8.34440i	1.06164	−	0.710322i
$139$		−	8.86933i		−	0.752286i	−0.926562	−	0.376143i	$-0.877250\pi$
$139$		−	8.86933i		−	0.752286i	0.926562	−	0.376143i	$-0.122750\pi$
$140$	−5.54808	−	18.7131i	−0.468898	−	1.58155i
$141$	12.6933	+	2.51666i	1.06897	+	0.211941i
$142$	28.2964	−	28.2964i	2.37458	−	2.37458i
$143$	3.39641	−	3.39641i	0.284022	−	0.284022i
$144$	−17.2276	+	41.7378i	−1.43564	+	3.47815i
$145$	9.49715	+	5.15351i	0.788695	+	0.427976i
$146$		−	23.1855i		−	1.91884i
$147$	−4.29654	−	6.42159i	−0.354373	−	0.529644i
$148$	−34.2091	−	34.2091i	−2.81197	−	2.81197i
$149$	−2.80986			−0.230192			−0.115096	−	0.993354i	$-0.536718\pi$
$149$	−2.80986			−0.230192			−0.115096	+	0.993354i	$0.536718\pi$
$150$	8.80002	+	21.9863i	0.718519	+	1.79518i
$151$	4.13581			0.336567			0.168284	−	0.985739i	$-0.446178\pi$
$151$	4.13581			0.336567			0.168284	+	0.985739i	$0.446178\pi$
$152$	11.7458	+	11.7458i	0.952712	+	0.952712i
$153$	7.20100	−	2.99324i	0.582167	−	0.241989i
$154$		−	3.06945i		−	0.247343i
$155$	−1.96536	−	1.06648i	−0.157861	−	0.0856615i
$156$	−12.5822	+	63.4610i	−1.00738	+	5.08095i
$157$	0.0365923	−	0.0365923i	0.00292038	−	0.00292038i	−0.705645	−	0.708565i	$-0.749343\pi$
$157$	0.0365923	−	0.0365923i	0.00292038	−	0.00292038i	0.708565	+	0.705645i	$0.249343\pi$
$158$	−22.7962	+	22.7962i	−1.81357	+	1.81357i
$159$	1.31820	−	6.64862i	0.104540	−	0.527270i
$160$	−14.0707	−	47.4591i	−1.11239	−	3.75197i
$161$		−	5.04835i		−	0.397865i
$162$	0.0611521	+	24.6110i	0.00480456	+	1.93362i
$163$	−11.4864	−	11.4864i	−0.899686	−	0.899686i	0.0957224	−	0.995408i	$-0.469484\pi$
$163$	−11.4864	−	11.4864i	−0.899686	−	0.899686i	−0.995408	+	0.0957224i	$0.969484\pi$
$164$	−30.0894			−2.34959
$165$	0.251987	+	2.71651i	0.0196172	+	0.211480i
$166$	32.5944			2.52981
$167$	−7.54391	−	7.54391i	−0.583765	−	0.583765i	0.352171	−	0.935936i	$-0.385444\pi$
$167$	−7.54391	−	7.54391i	−0.583765	−	0.583765i	−0.935936	+	0.352171i	$0.885444\pi$
$168$	14.5965	+	21.8158i	1.12614	+	1.68313i
$169$			33.4962i			2.57663i
$170$	−7.58088	+	13.9704i	−0.581427	+	1.07148i
$171$	4.84349	+	1.99920i	0.370391	+	0.152882i
$172$	−5.47532	+	5.47532i	−0.417489	+	0.417489i
$173$	−2.95265	+	2.95265i	−0.224486	+	0.224486i	−0.810384	−	0.585899i	$-0.800742\pi$
$173$	−2.95265	+	2.95265i	−0.224486	+	0.224486i	0.585899	+	0.810384i	$0.300742\pi$
$174$	−22.4506	−	4.45121i	−1.70198	−	0.337445i
$175$	7.79408	+	1.65268i	0.589177	+	0.124931i
$176$		−	10.6022i		−	0.799171i
$177$	−2.04755	+	1.36997i	−0.153903	+	0.102973i
$178$	23.2561	+	23.2561i	1.74312	+	1.74312i
$179$	10.7325			0.802185			0.401092	−	0.916038i	$-0.368631\pi$
$179$	10.7325			0.802185			0.401092	+	0.916038i	$0.368631\pi$
$180$	−23.1678	−	28.5230i	−1.72683	−	2.12598i
$181$	4.01997			0.298802			0.149401	−	0.988777i	$-0.452265\pi$
$181$	4.01997			0.298802			0.149401	+	0.988777i	$0.452265\pi$
$182$	21.0101	+	21.0101i	1.55737	+	1.55737i
$183$	−7.03155	+	4.70465i	−0.519787	+	0.347778i
$184$		−	30.1303i		−	2.22123i
$185$	18.9337	−	5.61349i	1.39204	−	0.412712i
$186$	4.64597	+	0.921141i	0.340659	+	0.0675414i
$187$	−1.29477	+	1.29477i	−0.0946828	+	0.0946828i
$188$	28.9389	−	28.9389i	2.11059	−	2.11059i
$189$	6.89308	+	4.58725i	0.501398	+	0.333673i
$190$	−10.2395	+	3.03581i	−0.742850	+	0.220241i
$191$		−	18.5014i		−	1.33872i	−0.742940	−	0.669358i	$-0.766569\pi$
$191$		−	18.5014i		−	1.33872i	0.742940	−	0.669358i	$-0.233431\pi$
$192$	29.3133	+	43.8115i	2.11551	+	3.16183i
$193$	4.56932	+	4.56932i	0.328907	+	0.328907i	0.852171	−	0.523264i	$-0.175286\pi$
$193$	4.56932	+	4.56932i	0.328907	+	0.328907i	−0.523264	+	0.852171i	$0.675286\pi$
$194$	−0.0963751			−0.00691933
$195$	−20.3191	−	16.8694i	−1.45508	−	1.20805i
$196$	−24.4358			−1.74541
$197$	5.02143	+	5.02143i	0.357762	+	0.357762i	0.862987	−	0.505226i	$-0.168591\pi$
$197$	5.02143	+	5.02143i	0.357762	+	0.357762i	−0.505226	+	0.862987i	$0.668591\pi$
$198$	−2.21807	−	5.33615i	−0.157632	−	0.379223i
$199$		−	3.15220i		−	0.223454i	−0.993739	−	0.111727i	$-0.964362\pi$
$199$		−	3.15220i		−	0.223454i	0.993739	−	0.111727i	$-0.0356381\pi$
$200$	46.5178	+	9.86377i	3.28930	+	0.697474i
$201$	3.27601	−	16.5233i	0.231072	−	1.16546i
$202$	−19.1040	+	19.1040i	−1.34415	+	1.34415i
$203$	−5.44480	+	5.44480i	−0.382150	+	0.382150i
$204$	4.79654	−	24.1924i	0.335825	−	1.69380i
$205$	5.85807	−	10.7956i	0.409146	−	0.753994i
$206$			11.6815i			0.813886i
$207$	−3.64808	−	8.77640i	−0.253559	−	0.610002i
$208$	72.5710	+	72.5710i	5.03189	+	5.03189i
$209$	−1.23034			−0.0851045
$210$	−16.8042	+	1.55878i	−1.15960	+	0.107566i
$211$	23.0125			1.58425			0.792124	−	0.610361i	$-0.208975\pi$
$211$	23.0125			1.58425			0.792124	+	0.610361i	$0.208975\pi$
$212$	−15.1579	−	15.1579i	−1.04105	−	1.04105i
$213$	−14.0948	−	21.0661i	−0.965763	−	1.44342i
$214$		−	32.9234i		−	2.25060i
$215$	−0.898465	−	3.03043i	−0.0612748	−	0.206674i
$216$	41.1403	+	27.3783i	2.79924	+	1.86286i
$217$	1.12676	−	1.12676i	0.0764893	−	0.0764893i
$218$	23.7545	−	23.7545i	1.60886	−	1.60886i
$219$	−14.4051	−	2.85605i	−0.973405	−	0.192994i
$220$	7.58365	+	4.11517i	0.511289	+	0.277445i
$221$		−	17.7251i		−	1.19232i
$222$	−34.7665	+	23.2615i	−2.33338	+	1.56121i
$223$	−9.93645	−	9.93645i	−0.665394	−	0.665394i	0.291252	−	0.956646i	$-0.405928\pi$
$223$	−9.93645	−	9.93645i	−0.665394	−	0.665394i	−0.956646	+	0.291252i	$0.905928\pi$
$224$	35.2756			2.35695
$225$	14.7441	−	2.75910i	0.982937	−	0.183940i
$226$	−2.09502			−0.139359
$227$	1.51169	+	1.51169i	0.100334	+	0.100334i	0.755492	−	0.655158i	$-0.227398\pi$
$227$	1.51169	+	1.51169i	0.100334	+	0.100334i	−0.655158	+	0.755492i	$0.727398\pi$
$228$	13.7732	−	9.21536i	0.912155	−	0.610302i
$229$			8.23863i			0.544424i	0.962237	+	0.272212i	$0.0877552\pi$
$229$			8.23863i			0.544424i	−0.962237	+	0.272212i	$0.912245\pi$
$230$	17.0268	+	9.23939i	1.12272	+	0.609227i
$231$	−1.90704	−	0.378103i	−0.125474	−	0.0248773i
$232$	−32.4964	+	32.4964i	−2.13350	+	2.13350i
$233$	−1.85236	+	1.85236i	−0.121352	+	0.121352i	−0.765175	−	0.643823i	$-0.777348\pi$
$233$	−1.85236	+	1.85236i	−0.121352	+	0.121352i	0.643823	+	0.765175i	$0.277348\pi$
$234$	51.7079	+	21.3429i	3.38025	+	1.39523i
$235$	4.74869	+	16.0169i	0.309770	+	1.04482i
$236$			7.79144i			0.507179i
$237$	11.3551	+	16.9713i	0.737594	+	1.10240i
$238$	−8.00938	−	8.00938i	−0.519171	−	0.519171i
$239$	7.32482			0.473803			0.236902	−	0.971534i	$-0.423868\pi$
$239$	7.32482			0.473803			0.236902	+	0.971534i	$0.423868\pi$
$240$	−58.0436	+	5.38421i	−3.74670	+	0.347549i
$241$	−19.7394			−1.27153			−0.635763	−	0.771884i	$-0.719314\pi$
$241$	−19.7394			−1.27153			−0.635763	+	0.771884i	$0.719314\pi$
$242$	−20.3105	−	20.3105i	−1.30561	−	1.30561i
$243$	15.2983	+	2.99366i	0.981386	+	0.192043i
$244$			26.7568i			1.71293i
$245$	4.75738	−	8.76713i	0.303938	−	0.560112i
$246$	−5.05976	+	25.5200i	−0.322598	+	1.62709i
$247$	8.42157	−	8.42157i	0.535852	−	0.535852i
$248$	6.72487	−	6.72487i	0.427030	−	0.427030i
$249$	4.01506	−	20.2508i	0.254444	−	1.28334i
$250$	−19.8387	+	23.2628i	−1.25471	+	1.47127i
$251$		−	18.6805i		−	1.17911i	−0.807730	−	0.589553i	$-0.799304\pi$
$251$		−	18.6805i		−	1.17911i	0.807730	−	0.589553i	$-0.200696\pi$
$252$	24.1807	−	10.0512i	1.52324	−	0.633164i
$253$	1.57803	+	1.57803i	0.0992099	+	0.0992099i
$254$	58.3492			3.66115
$255$	7.74597	+	6.43090i	0.485071	+	0.402719i
$256$	45.6410			2.85256
$257$	10.4990	+	10.4990i	0.654909	+	0.654909i	0.954171	−	0.299262i	$-0.0967405\pi$
$257$	10.4990	+	10.4990i	0.654909	+	0.654909i	−0.299262	+	0.954171i	$0.596741\pi$
$258$	3.72311	+	5.56454i	0.231791	+	0.346433i
$259$			14.0732i			0.874464i
$260$	−80.0773	+	23.7414i	−4.96618	+	1.47238i
$261$	−5.53105	+	13.4002i	−0.342363	+	0.829452i
$262$	−2.74642	+	2.74642i	−0.169674	+	0.169674i
$263$	2.04156	−	2.04156i	0.125888	−	0.125888i	−0.641356	−	0.767244i	$-0.721628\pi$
$263$	2.04156	−	2.04156i	0.125888	−	0.125888i	0.767244	+	0.641356i	$0.221628\pi$
$264$	−11.3819	−	2.25665i	−0.700506	−	0.138887i
$265$	8.38946	−	2.48731i	0.515360	−	0.152794i
$266$		−	7.61085i		−	0.466651i
$267$	17.3137	−	11.5842i	1.05958	−	0.708942i
$268$	−37.6706	−	37.6706i	−2.30110	−	2.30110i
$269$	−7.42815			−0.452903			−0.226451	−	0.974022i	$-0.572712\pi$
$269$	−7.42815			−0.452903			−0.226451	+	0.974022i	$0.572712\pi$
$270$	−28.0873	+	14.8531i	−1.70934	+	0.903934i
$271$	−9.00413			−0.546962			−0.273481	−	0.961877i	$-0.588175\pi$
$271$	−9.00413			−0.546962			−0.273481	+	0.961877i	$0.588175\pi$
$272$	−27.6652	−	27.6652i	−1.67745	−	1.67745i
$273$	15.6416	−	10.4654i	0.946672	−	0.633397i
$274$		−	10.9422i		−	0.661042i
$275$	−2.95290	+	1.91970i	−0.178067	+	0.115762i
$276$	−29.4851	−	5.84590i	−1.77479	−	0.351882i
$277$	−4.37266	+	4.37266i	−0.262728	+	0.262728i	−0.826161	−	0.563434i	$-0.809480\pi$
$277$	−4.37266	+	4.37266i	−0.262728	+	0.262728i	0.563434	+	0.826161i	$0.309480\pi$
$278$	−17.1500	+	17.1500i	−1.02859	+	1.02859i
$279$	1.14461	−	2.77306i	0.0685258	−	0.166019i
$280$	−16.1620	+	29.7842i	−0.965866	+	1.77995i
$281$			30.7914i			1.83686i	0.395582	+	0.918431i	$0.370543\pi$
$281$			30.7914i			1.83686i	−0.395582	+	0.918431i	$0.629457\pi$
$282$	−19.6779	−	29.4105i	−1.17180	−	1.75137i
$283$	−12.0318	−	12.0318i	−0.715214	−	0.715214i	0.252407	−	0.967621i	$-0.418778\pi$
$283$	−12.0318	−	12.0318i	−0.715214	−	0.715214i	−0.967621	+	0.252407i	$0.918778\pi$
$284$	−80.1618			−4.75673
$285$	0.624815	+	6.73572i	0.0370108	+	0.398990i
$286$	−13.1348			−0.776678
$287$	6.18919	+	6.18919i	0.365336	+	0.365336i
$288$	61.3256	−	25.4912i	3.61364	−	1.50208i
$289$		−	10.2429i		−	0.602523i
$290$	−8.39899	−	28.3289i	−0.493206	−	1.66353i
$291$	−0.0118717	+	0.0598776i	−0.000695933	+	0.00351009i
$292$	−32.8415	+	32.8415i	−1.92190	+	1.92190i
$293$	−15.2115	+	15.2115i	−0.888663	+	0.888663i	−0.994395	−	0.105732i	$-0.966281\pi$
$293$	−15.2115	+	15.2115i	−0.888663	+	0.888663i	0.105732	+	0.994395i	$0.466281\pi$
$294$	−4.10906	+	20.7249i	−0.239645	+	1.20870i
$295$	−2.79543	−	1.51691i	−0.162756	−	0.0883177i
$296$			83.9934i			4.88202i
$297$	−3.58856	+	0.720764i	−0.208230	+	0.0418230i
$298$	5.43322	+	5.43322i	0.314738	+	0.314738i
$299$	−21.6029			−1.24933
$300$	18.6780	−	43.6079i	1.07837	−	2.51770i
$301$	2.25247			0.129830
$302$	−7.99712	−	7.99712i	−0.460182	−	0.460182i
$303$	9.51597	+	14.2225i	0.546678	+	0.817063i
$304$		−	26.2887i		−	1.50776i
$305$	−9.59988	−	5.20925i	−0.549687	−	0.298281i
$306$	−19.7119	−	8.13626i	−1.12685	−	0.465119i
$307$	6.07251	−	6.07251i	0.346576	−	0.346576i	−0.512256	−	0.858833i	$-0.671190\pi$
$307$	6.07251	−	6.07251i	0.346576	−	0.346576i	0.858833	+	0.512256i	$0.171190\pi$
$308$	−4.34778	+	4.34778i	−0.247738	+	0.247738i
$309$	7.25767	+	1.43895i	0.412874	+	0.0818592i
$310$	1.73810	+	5.86244i	0.0987176	+	0.332964i
$311$			4.62811i			0.262436i	0.991354	+	0.131218i	$0.0418888\pi$
$311$			4.62811i			0.262436i	−0.991354	+	0.131218i	$0.958111\pi$
$312$	93.3544	−	62.4613i	5.28515	−	3.53617i
$313$	−13.9086	−	13.9086i	−0.786161	−	0.786161i	0.194701	−	0.980863i	$-0.437626\pi$
$313$	−13.9086	−	13.9086i	−0.786161	−	0.786161i	−0.980863	+	0.194701i	$0.937626\pi$
$314$	−0.141512			−0.00798598
$315$	−1.10152	+	10.6325i	−0.0620637	+	0.599071i
$316$	64.5801			3.63291
$317$	5.08343	+	5.08343i	0.285514	+	0.285514i	0.835303	−	0.549790i	$-0.185292\pi$
$317$	5.08343	+	5.08343i	0.285514	+	0.285514i	−0.549790	+	0.835303i	$0.685292\pi$
$318$	−15.4049	+	10.3071i	−0.863863	+	0.577991i
$319$		−	3.40391i		−	0.190582i
$320$	−32.4574	+	59.8141i	−1.81442	+	3.34371i
$321$	−20.4552	−	4.05559i	−1.14170	−	0.226361i
$322$	−9.76163	+	9.76163i	−0.543994	+	0.543994i
$323$	−3.21044	+	3.21044i	−0.178634	+	0.178634i
$324$	34.7741	−	34.9473i	1.93189	−	1.94152i
$325$	7.07217	−	33.3525i	0.392293	−	1.85006i
$326$			44.4210i			2.46025i
$327$	−11.8325	−	17.6848i	−0.654339	−	0.977971i
$328$	36.9392	+	36.9392i	2.03963	+	2.03963i
$329$	−11.9051			−0.656348
$330$	4.76548	−	5.73998i	0.262331	−	0.315976i
$331$	−25.8277			−1.41962			−0.709809	−	0.704394i	$-0.751219\pi$
$331$	−25.8277			−1.41962			−0.709809	+	0.704394i	$0.751219\pi$
$332$	−46.1689	−	46.1689i	−2.53385	−	2.53385i
$333$	10.1697	+	24.4658i	0.557295	+	1.34072i
$334$			29.1743i			1.59634i
$335$	20.8496	−	6.18151i	1.13914	−	0.337732i
$336$	8.07891	−	40.7477i	0.440741	−	2.22297i
$337$	−11.2502	+	11.2502i	−0.612837	+	0.612837i	−0.943684	−	0.330848i	$-0.892665\pi$
$337$	−11.2502	+	11.2502i	−0.612837	+	0.612837i	0.330848	+	0.943684i	$0.392665\pi$
$338$	64.7693	−	64.7693i	3.52298	−	3.52298i
$339$	−0.258070	+	1.30163i	−0.0140164	+	0.0706949i
$340$	30.5268	−	9.05060i	1.65555	−	0.490838i
$341$			0.704412i			0.0381460i
$342$	−5.49982	−	13.2312i	−0.297396	−	0.715463i
$343$	12.9136	+	12.9136i	0.697268	+	0.697268i
$344$	13.4435			0.724827
$345$	7.83782	−	9.44059i	0.421974	−	0.508264i
$346$	11.4187			0.613871
$347$	4.48313	+	4.48313i	0.240667	+	0.240667i	0.817126	−	0.576459i	$-0.195566\pi$
$347$	4.48313	+	4.48313i	0.240667	+	0.240667i	−0.576459	+	0.817126i	$0.695566\pi$
$348$	25.4956	+	38.1056i	1.36671	+	2.04267i
$349$			31.3177i			1.67640i	0.545365	+	0.838199i	$0.316391\pi$
$349$			31.3177i			1.67640i	−0.545365	+	0.838199i	$0.683609\pi$
$350$	−11.8752	−	18.2665i	−0.634756	−	0.976388i
$351$	19.6298	−	29.4969i	1.04776	−	1.57443i
$352$	−11.0266	+	11.0266i	−0.587718	+	0.587718i
$353$	−7.74450	+	7.74450i	−0.412198	+	0.412198i	−0.882504	−	0.470306i	$-0.844144\pi$
$353$	−7.74450	+	7.74450i	−0.412198	+	0.412198i	0.470306	+	0.882504i	$0.344144\pi$
$354$	6.60821	+	1.31019i	0.351222	+	0.0696357i
$355$	15.6066	−	28.7606i	0.828313	−	1.52646i
$356$		−	65.8830i		−	3.49179i
$357$	−5.96283	+	3.98959i	−0.315586	+	0.211152i
$358$	−20.7527	−	20.7527i	−1.09681	−	1.09681i
$359$	7.01325			0.370145			0.185073	−	0.982725i	$-0.440748\pi$
$359$	7.01325			0.370145			0.185073	+	0.982725i	$0.440748\pi$
$360$	−6.57426	+	63.4581i	−0.346494	+	3.34454i
$361$	15.9493			0.839437
$362$	−7.77313	−	7.77313i	−0.408547	−	0.408547i
$363$	−15.1207	+	10.1170i	−0.793633	+	0.531002i
$364$		−	59.5202i		−	3.11971i
$365$	−5.38908	−	18.1768i	−0.282077	−	0.951418i
$366$	22.6935	+	4.49936i	1.18621	+	0.235185i
$367$	−7.10790	+	7.10790i	−0.371029	+	0.371029i	−0.867852	−	0.496823i	$-0.834500\pi$
$367$	−7.10790	+	7.10790i	−0.371029	+	0.371029i	0.496823	+	0.867852i	$0.334500\pi$
$368$	−33.7177	+	33.7177i	−1.75766	+	1.75766i
$369$	15.2322	+	6.28723i	0.792958	+	0.327300i
$370$	−47.4653	−	25.7564i	−2.46760	−	1.33901i
$371$			6.23575i			0.323744i
$372$	−5.27610	−	7.88564i	−0.273553	−	0.408851i
$373$	12.4652	+	12.4652i	0.645426	+	0.645426i	0.951884	−	0.306458i	$-0.0991440\pi$
$373$	12.4652	+	12.4652i	0.645426	+	0.645426i	−0.306458	+	0.951884i	$0.599144\pi$
$374$	5.00720			0.258916
$375$	12.0093	+	15.1913i	0.620160	+	0.784475i
$376$	−71.0536			−3.66431
$377$	23.2994	+	23.2994i	1.19998	+	1.19998i
$378$	−4.45862	−	22.1987i	−0.229327	−	1.14178i
$379$		−	22.8420i		−	1.17332i	−0.809835	−	0.586658i	$-0.800443\pi$
$379$		−	22.8420i		−	1.17332i	0.809835	−	0.586658i	$-0.199557\pi$
$380$	18.8040	+	10.2038i	0.964626	+	0.523442i
$381$	7.18761	−	36.2522i	0.368232	−	1.85726i
$382$	−35.7749	+	35.7749i	−1.83040	+	1.83040i
$383$	−4.23470	+	4.23470i	−0.216383	+	0.216383i	−0.806972	−	0.590589i	$-0.798895\pi$
$383$	−4.23470	+	4.23470i	−0.216383	+	0.216383i	0.590589	+	0.806972i	$0.298895\pi$
$384$	13.1201	−	66.1741i	0.669533	−	3.37693i
$385$	−0.713442	−	2.40637i	−0.0363604	−	0.122640i
$386$		−	17.6707i		−	0.899417i
$387$	3.91586	−	1.62770i	0.199054	−	0.0827409i
$388$	0.136512	+	0.136512i	0.00693036	+	0.00693036i
$389$	−36.8239			−1.86705			−0.933524	−	0.358515i	$-0.883283\pi$
$389$	−36.8239			−1.86705			−0.933524	+	0.358515i	$0.883283\pi$
$390$	6.67036	+	71.9088i	0.337767	+	3.64125i
$391$	8.23538			0.416481
$392$	29.9986	+	29.9986i	1.51516	+	1.51516i
$393$	1.36803	+	2.04465i	0.0690081	+	0.103139i
$394$		−	19.4192i		−	0.978323i
$395$	−12.5730	+	23.1702i	−0.632618	+	1.16582i
$396$	−4.41665	+	10.7003i	−0.221945	+	0.537711i
$397$	1.82340	−	1.82340i	0.0915136	−	0.0915136i	−0.659868	−	0.751382i	$-0.729388\pi$
$397$	1.82340	−	1.82340i	0.0915136	−	0.0915136i	0.751382	+	0.659868i	$0.229388\pi$
$398$	−6.09519	+	6.09519i	−0.305524	+	0.305524i
$399$	−4.72860	−	0.937524i	−0.236726	−	0.0469349i
$400$	−41.0182	−	63.0946i	−2.05091	−	3.15473i
$401$			13.9250i			0.695384i	0.937609	+	0.347692i	$0.113034\pi$
$401$			13.9250i			0.695384i	−0.937609	+	0.347692i	$0.886966\pi$
$402$	−38.2845	+	25.6153i	−1.90946	+	1.27757i
$403$	−4.82163	−	4.82163i	−0.240182	−	0.240182i
$404$	54.1203			2.69259
$405$	5.76836	+	19.2802i	0.286632	+	0.958041i
$406$	21.0565			1.04501
$407$	−4.39904	−	4.39904i	−0.218052	−	0.218052i
$408$	−35.5882	+	23.8113i	−1.76188	+	1.17883i
$409$			20.1681i			0.997248i	0.866818	+	0.498624i	$0.166161\pi$
$409$			20.1681i			0.997248i	−0.866818	+	0.498624i	$0.833839\pi$
$410$	−32.2020	+	9.54726i	−1.59034	+	0.471506i
$411$	−6.79836	−	1.34789i	−0.335338	−	0.0664864i
$412$	16.5464	−	16.5464i	0.815184	−	0.815184i
$413$	1.60265	−	1.60265i	0.0788611	−	0.0788611i
$414$	−9.91626	+	24.0244i	−0.487358	+	1.18073i
$415$	25.5532	−	7.57602i	1.25436	−	0.371892i
$416$		−	150.952i		−	7.40101i
$417$	8.54267	+	12.7678i	0.418336	+	0.625244i
$418$	2.37903	+	2.37903i	0.116362	+	0.116362i
$419$	5.84177			0.285389			0.142695	−	0.989767i	$-0.454423\pi$
$419$	5.84177			0.285389			0.142695	+	0.989767i	$0.454423\pi$
$420$	26.0106	+	21.5947i	1.26919	+	1.05371i
$421$	−4.63552			−0.225921			−0.112961	−	0.993599i	$-0.536033\pi$
$421$	−4.63552			−0.225921			−0.112961	+	0.993599i	$0.536033\pi$
$422$	−44.4977	−	44.4977i	−2.16611	−	2.16611i
$423$	−20.6966	+	8.60296i	−1.00630	+	0.418290i
$424$			37.2171i			1.80742i
$425$	−2.69602	+	12.7145i	−0.130776	+	0.616745i
$426$	−13.4798	+	67.9882i	−0.653098	+	3.29404i
$427$	5.50370	−	5.50370i	0.266343	−	0.266343i
$428$	−46.6349	+	46.6349i	−2.25418	+	2.25418i
$429$	−1.61798	+	8.16063i	−0.0781168	+	0.393999i
$430$	−4.12244	+	7.59703i	−0.198802	+	0.366362i
$431$			22.2597i			1.07221i	0.844151	+	0.536105i	$0.180105\pi$
$431$			22.2597i			1.07221i	−0.844151	+	0.536105i	$0.819895\pi$
$432$	−15.4005	−	76.6767i	−0.740959	−	3.68911i
$433$	−10.3136	−	10.3136i	−0.495638	−	0.495638i	0.414439	−	0.910077i	$-0.363978\pi$
$433$	−10.3136	−	10.3136i	−0.495638	−	0.495638i	−0.910077	+	0.414439i	$0.863978\pi$
$434$	−4.35746			−0.209165
$435$	−18.6353	+	1.72864i	−0.893495	+	0.0828818i
$436$	−67.2951			−3.22285
$437$	3.91280	+	3.91280i	0.187175	+	0.187175i
$438$	22.3316	+	33.3766i	1.06704	+	1.59480i
$439$		−	18.3671i		−	0.876613i	−0.898826	−	0.438307i	$-0.855578\pi$
$439$		−	18.3671i		−	0.876613i	0.898826	−	0.438307i	$-0.144422\pi$
$440$	−4.25807	−	14.3620i	−0.202995	−	0.684683i
$441$	12.3702	+	5.10590i	0.589056	+	0.243138i
$442$	−34.2738	+	34.2738i	−1.63024	+	1.63024i
$443$	14.0924	−	14.0924i	0.669552	−	0.669552i	−0.288060	−	0.957612i	$-0.593010\pi$
$443$	14.0924	−	14.0924i	0.669552	−	0.669552i	0.957612	+	0.288060i	$0.0930104\pi$
$444$	82.1948	+	16.2965i	3.90079	+	0.773397i
$445$	23.6377	+	12.8267i	1.12053	+	0.608043i
$446$			38.4268i			1.81956i
$447$	4.04493	−	2.70637i	0.191319	−	0.128007i
$448$	−34.2920	−	34.2920i	−1.62014	−	1.62014i
$449$	−11.1950			−0.528325			−0.264163	−	0.964478i	$-0.585096\pi$
$449$	−11.1950			−0.528325			−0.264163	+	0.964478i	$0.585096\pi$
$450$	−33.8446	−	23.1745i	−1.59545	−	1.09246i
$451$	−3.86928			−0.182197
$452$	2.96753	+	2.96753i	0.139581	+	0.139581i
$453$	−5.95370	+	3.98349i	−0.279729	+	0.187160i
$454$		−	5.84610i		−	0.274371i
$455$	21.3548	+	11.5879i	1.00113	+	0.543250i
$456$	−28.2219	−	5.59547i	−1.32161	−	0.262032i
$457$	21.3153	−	21.3153i	0.997087	−	0.997087i	−0.00290829	−	0.999996i	$-0.500926\pi$
$457$	21.3153	−	21.3153i	0.997087	−	0.997087i	0.999996	+	0.00290829i	$0.000925739\pi$
$458$	15.9305	−	15.9305i	0.744382	−	0.744382i
$459$	−7.48320	+	11.2447i	−0.349286	+	0.524858i
$460$	−11.0306	−	37.2052i	−0.514306	−	1.73470i
$461$		−	33.6981i		−	1.56948i	−0.619827	−	0.784738i	$-0.712797\pi$
$461$		−	33.6981i		−	1.56948i	0.619827	−	0.784738i	$-0.287203\pi$
$462$	2.95640	+	4.41862i	0.137544	+	0.205573i
$463$	9.27527	+	9.27527i	0.431058	+	0.431058i	0.888988	−	0.457930i	$-0.151409\pi$
$463$	9.27527	+	9.27527i	0.431058	+	0.431058i	−0.457930	+	0.888988i	$0.651409\pi$
$464$	72.7312			3.37646
$465$	3.85643	−	0.357727i	0.178838	−	0.0165892i
$466$	7.16357			0.331846
$467$	18.2501	+	18.2501i	0.844515	+	0.844515i	0.989442	−	0.144927i	$-0.0462949\pi$
$467$	18.2501	+	18.2501i	0.844515	+	0.844515i	−0.144927	+	0.989442i	$0.546295\pi$
$468$	−43.0111	−	103.474i	−1.98819	−	4.78309i
$469$			15.4972i			0.715594i
$470$	21.7885	−	40.1529i	1.00503	−	1.85211i
$471$	−0.0174318	+	0.0879211i	−0.000803216	+	0.00405119i
$472$	9.56515	−	9.56515i	0.440272	−	0.440272i
$473$	−0.704086	+	0.704086i	−0.0323739	+	0.0323739i
$474$	10.8596	−	54.7728i	0.498799	−	2.51580i
$475$	−7.32187	+	4.75999i	−0.335950	+	0.218403i
$476$			22.6901i			1.04000i
$477$	4.50614	+	10.8407i	0.206322	+	0.496360i
$478$	−14.1635	−	14.1635i	−0.647823	−	0.647823i
$479$	−32.4048			−1.48061			−0.740306	−	0.672270i	$-0.765319\pi$
$479$	−32.4048			−1.48061			−0.740306	+	0.672270i	$0.765319\pi$
$480$	65.9666	+	54.7672i	3.01095	+	2.49977i
$481$	60.2220			2.74589
$482$	38.1687	+	38.1687i	1.73854	+	1.73854i
$483$	4.86242	+	7.26734i	0.221248	+	0.330676i
$484$			57.5383i			2.61538i
$485$	−0.0755556	+	0.0224008i	−0.00343080	+	0.00101717i
$486$	−23.7926	−	35.3699i	−1.07926	−	1.60441i
$487$	−10.1603	+	10.1603i	−0.460405	+	0.460405i	−0.898788	−	0.438383i	$-0.855551\pi$
$487$	−10.1603	+	10.1603i	−0.460405	+	0.460405i	0.438383	+	0.898788i	$0.355551\pi$
$488$	32.8480	−	32.8480i	1.48696	−	1.48696i
$489$	27.5986	+	5.47189i	1.24805	+	0.247447i
$490$	−26.1514	+	7.75339i	−1.18140	+	0.350262i
$491$			0.554814i			0.0250384i	0.999922	+	0.0125192i	$0.00398509\pi$
$491$			0.554814i			0.0250384i	−0.999922	+	0.0125192i	$0.996015\pi$
$492$	43.3152	−	28.9812i	1.95280	−	1.30657i
$493$	−8.88213	−	8.88213i	−0.400031	−	0.400031i
$494$	−32.5684			−1.46532
$495$	−2.97921	−	3.66785i	−0.133906	−	0.164858i
$496$	−15.0511			−0.675816
$497$	16.4887	+	16.4887i	0.739621	+	0.739621i
$498$	−46.9212	+	31.3939i	−2.10259	+	1.40680i
$499$		−	7.71945i		−	0.345570i	−0.984960	−	0.172785i	$-0.944723\pi$
$499$		−	7.71945i		−	0.345570i	0.984960	−	0.172785i	$-0.0552766\pi$
$500$	61.0519	−	4.85017i	2.73032	−	0.216906i
$501$	18.1259	+	3.59376i	0.809806	+	0.160557i
$502$	−36.1213	+	36.1213i	−1.61217	+	1.61217i
$503$	−18.6078	+	18.6078i	−0.829681	+	0.829681i	−0.987473	−	0.157791i	$-0.949563\pi$
$503$	−18.6078	+	18.6078i	−0.829681	+	0.829681i	0.157791	+	0.987473i	$0.449563\pi$
$504$	−42.0247	−	17.3461i	−1.87193	−	0.772655i
$505$	−10.5366	+	19.4174i	−0.468873	+	0.864064i
$506$		−	6.10265i		−	0.271296i
$507$	−32.2626	−	48.2195i	−1.43283	−	2.14150i
$508$	−82.6498	−	82.6498i	−3.66699	−	3.66699i
$509$	−22.1578			−0.982126			−0.491063	−	0.871124i	$-0.663391\pi$
$509$	−22.1578			−0.982126			−0.491063	+	0.871124i	$0.663391\pi$
$510$	−2.54285	−	27.4128i	−0.112599	−	1.21386i
$511$	13.5105			0.597671
$512$	−33.1702	−	33.1702i	−1.46593	−	1.46593i
$513$	−8.89802	+	1.78717i	−0.392857	+	0.0789055i
$514$		−	40.6023i		−	1.79089i
$515$	2.71516	+	9.15797i	0.119644	+	0.403548i
$516$	2.60833	−	13.1557i	0.114825	−	0.579146i
$517$	3.72133	−	3.72133i	0.163664	−	0.163664i
$518$	27.2123	−	27.2123i	1.19564	−	1.19564i
$519$	1.40658	−	7.09439i	0.0617421	−	0.311409i
$520$	127.453	+	69.1607i	5.58918	+	3.03290i
$521$		−	42.7144i		−	1.87135i	−0.352863	−	0.935675i	$-0.614792\pi$
$521$		−	42.7144i		−	1.87135i	0.352863	−	0.935675i	$-0.385208\pi$
$522$	36.6060	−	15.2160i	1.60220	−	0.665987i
$523$	3.75838	+	3.75838i	0.164343	+	0.164343i	0.784487	−	0.620145i	$-0.212926\pi$
$523$	3.75838	+	3.75838i	0.164343	+	0.164343i	−0.620145	+	0.784487i	$0.712926\pi$
$524$	7.78043			0.339889
$525$	−12.8118	+	5.12791i	−0.559152	+	0.223801i
$526$	−7.89525			−0.344249
$527$	1.83808	+	1.83808i	0.0800682	+	0.0800682i
$528$	10.2117	+	15.2624i	0.444408	+	0.664210i
$529$			12.9629i			0.563605i
$530$	−21.0316	−	11.4126i	−0.913556	−	0.495730i
$531$	1.62803	−	3.94427i	0.0706507	−	0.171167i
$532$	−10.7805	+	10.7805i	−0.467395	+	0.467395i
$533$	26.4848	−	26.4848i	1.14719	−	1.14719i
$534$	−55.8778	−	11.0787i	−2.41807	−	0.479423i
$535$	−7.65249	−	25.8111i	−0.330846	−	1.11591i
$536$			92.4926i			3.99507i
$537$	−15.4500	+	10.3372i	−0.666715	+	0.446084i
$538$	14.3633	+	14.3633i	0.619246	+	0.619246i
$539$	−3.14227			−0.135347
$540$	60.8237	+	18.7457i	2.61744	+	0.806686i
$541$	−19.5017			−0.838445			−0.419223	−	0.907883i	$-0.637697\pi$
$541$	−19.5017			−0.838445			−0.419223	+	0.907883i	$0.637697\pi$
$542$	17.4107	+	17.4107i	0.747852	+	0.747852i
$543$	−5.78694	+	3.87191i	−0.248341	+	0.166160i
$544$			57.5452i			2.46723i
$545$	13.1016	−	24.1443i	0.561211	−	1.03423i
$546$	−50.4813	−	10.0088i	−2.16040	−	0.428336i
$547$	8.53154	−	8.53154i	0.364782	−	0.364782i	−0.500788	−	0.865570i	$-0.666956\pi$
$547$	8.53154	−	8.53154i	0.364782	−	0.364782i	0.865570	+	0.500788i	$0.166956\pi$
$548$	−15.4993	+	15.4993i	−0.662096	+	0.662096i
$549$	5.59088	−	13.5452i	0.238613	−	0.578093i
$550$	9.42182	+	1.99783i	0.401748	+	0.0851878i
$551$		−	8.44016i		−	0.359563i
$552$	29.0206	+	43.3740i	1.23520	+	1.84612i
$553$	−13.2837	−	13.2837i	−0.564880	−	0.564880i
$554$	16.9102			0.718446
$555$	−21.8493	+	26.3173i	−0.927452	+	1.11711i
$556$	48.5848			2.06046
$557$	−5.37770	−	5.37770i	−0.227861	−	0.227861i	0.583938	−	0.811798i	$-0.301511\pi$
$557$	−5.37770	−	5.37770i	−0.227861	−	0.227861i	−0.811798	+	0.583938i	$0.801511\pi$
$558$	−7.57532	+	3.14883i	−0.320689	+	0.133301i
$559$		−	9.63880i		−	0.407678i
$560$	51.4168	−	15.2441i	2.17276	−	0.644181i
$561$	0.616801	−	3.11096i	0.0260413	−	0.131345i
$562$	59.5392	−	59.5392i	2.51151	−	2.51151i
$563$	−10.1122	+	10.1122i	−0.426178	+	0.426178i	−0.887324	−	0.461146i	$-0.847438\pi$
$563$	−10.1122	+	10.1122i	−0.426178	+	0.426178i	0.461146	+	0.887324i	$0.347438\pi$
$564$	−13.7859	+	69.5321i	−0.580491	+	2.92783i
$565$	−1.64244	+	0.486953i	−0.0690981	+	0.0204863i
$566$			46.5299i			1.95580i
$567$	−14.3412	+	0.0356343i	−0.602275	+	0.00149650i
$568$	98.4105	+	98.4105i	4.12921	+	4.12921i
$569$	−3.27264			−0.137196			−0.0685982	−	0.997644i	$-0.521853\pi$
$569$	−3.27264			−0.137196			−0.0685982	+	0.997644i	$0.521853\pi$
$570$	11.8162	−	14.2326i	0.494928	−	0.596136i
$571$	−16.4203			−0.687168			−0.343584	−	0.939122i	$-0.611641\pi$
$571$	−16.4203			−0.687168			−0.343584	+	0.939122i	$0.611641\pi$
$572$	18.6050	+	18.6050i	0.777916	+	0.777916i
$573$	17.8200	+	26.6337i	0.744442	+	1.11264i
$574$		−	23.9352i		−	0.999036i
$575$	15.4961	+	3.28585i	0.646233	+	0.137029i
$576$	−84.3960	−	34.8352i	−3.51650	−	1.45147i
$577$	16.2388	−	16.2388i	0.676029	−	0.676029i	−0.283070	−	0.959099i	$-0.591353\pi$
$577$	16.2388	−	16.2388i	0.676029	−	0.676029i	0.959099	+	0.283070i	$0.0913529\pi$
$578$	−19.8060	+	19.8060i	−0.823820	+	0.823820i
$579$	−10.9788	−	2.17673i	−0.456263	−	0.0904617i
$580$	−28.2301	+	52.0239i	−1.17219	+	2.16018i
$581$			18.9933i			0.787974i
$582$	0.138737	−	0.0928256i	0.00575082	−	0.00384775i
$583$	−1.94919	−	1.94919i	−0.0807274	−	0.0807274i
$584$	80.6356			3.33672
$585$	45.4985	+	4.71364i	1.88113	+	0.194885i
$586$	58.8267			2.43011
$587$	6.59866	+	6.59866i	0.272356	+	0.272356i	0.830048	−	0.557692i	$-0.188313\pi$
$587$	6.59866	+	6.59866i	0.272356	+	0.272356i	−0.557692	+	0.830048i	$0.688313\pi$
$588$	35.1765	−	23.5358i	1.45066	−	0.970601i
$589$			1.74662i			0.0719683i
$590$	2.47219	+	8.33847i	0.101779	+	0.343289i
$591$	−12.0651	−	2.39210i	−0.496291	−	0.0983980i
$592$	93.9941	−	93.9941i	3.86313	−	3.86313i
$593$	9.33347	−	9.33347i	0.383280	−	0.383280i	−0.489003	−	0.872282i	$-0.662639\pi$
$593$	9.33347	−	9.33347i	0.383280	−	0.383280i	0.872282	+	0.489003i	$0.162639\pi$
$594$	8.33265	+	5.54526i	0.341893	+	0.227525i
$595$	−8.14080	−	4.41750i	−0.333740	−	0.181100i
$596$		−	15.3920i		−	0.630480i
$597$	3.03611	+	4.53775i	0.124260	+	0.185718i
$598$	41.7721	+	41.7721i	1.70819	+	1.70819i
$599$	−23.7487			−0.970348			−0.485174	−	0.874418i	$-0.661244\pi$
$599$	−23.7487			−0.970348			−0.485174	+	0.874418i	$0.661244\pi$
$600$	−76.4651	+	30.6052i	−3.12168	+	1.24945i
$601$	−31.2501			−1.27472			−0.637360	−	0.770566i	$-0.719973\pi$
$601$	−31.2501			−1.27472			−0.637360	+	0.770566i	$0.719973\pi$
$602$	−4.35545	−	4.35545i	−0.177515	−	0.177515i
$603$	11.1987	+	26.9414i	0.456048	+	1.09714i
$604$			22.6553i			0.921832i
$605$	−20.6437	−	11.2021i	−0.839287	−	0.455429i
$606$	9.10073	−	45.9015i	0.369692	−	1.86462i
$607$	28.4393	−	28.4393i	1.15431	−	1.15431i	0.168635	−	0.985679i	$-0.446064\pi$
$607$	28.4393	−	28.4393i	1.15431	−	1.15431i	0.985679	−	0.168635i	$-0.0539360\pi$
$608$	−27.3409	+	27.3409i	−1.10882	+	1.10882i
$609$	2.59379	−	13.0823i	0.105106	−	0.530123i
$610$	8.48984	+	28.6354i	0.343744	+	1.15941i
$611$			50.9443i			2.06099i
$612$	16.3965	+	39.4460i	0.662790	+	1.59451i
$613$	−23.7604	−	23.7604i	−0.959673	−	0.959673i	0.0395446	−	0.999218i	$-0.487409\pi$
$613$	−23.7604	−	23.7604i	−0.959673	−	0.959673i	−0.999218	+	0.0395446i	$0.987409\pi$
$614$	−23.4840			−0.947736
$615$	1.96497	+	21.1831i	0.0792352	+	0.854183i
$616$	10.6751			0.430111
$617$	−27.8802	−	27.8802i	−1.12242	−	1.12242i	−0.991377	−	0.131039i	$-0.958169\pi$
$617$	−27.8802	−	27.8802i	−1.12242	−	1.12242i	−0.131039	−	0.991377i	$-0.541831\pi$
$618$	−11.2512	−	16.8160i	−0.452591	−	0.676441i
$619$		−	11.4690i		−	0.460980i	−0.973075	−	0.230490i	$-0.925967\pi$
$619$		−	11.4690i		−	0.460980i	0.973075	−	0.230490i	$-0.0740328\pi$
$620$	5.84200	−	10.7659i	0.234620	−	0.432370i
$621$	13.7048	+	9.12034i	0.549953	+	0.365986i
$622$	8.94906	−	8.94906i	0.358825	−	0.358825i
$623$	−13.5517	+	13.5517i	−0.542937	+	0.542937i
$624$	−174.368	−	34.5713i	−6.98030	−	1.38396i
$625$	−10.1460	+	22.8486i	−0.405839	+	0.913945i
$626$			53.7882i			2.14981i
$627$	1.77114	−	1.18503i	0.0707324	−	0.0473255i
$628$	0.200447	+	0.200447i	0.00799871	+	0.00799871i
$629$	−22.9576			−0.915379
$630$	22.6892	−	18.4293i	0.903958	−	0.734241i
$631$	−23.1740			−0.922543			−0.461272	−	0.887259i	$-0.652607\pi$
$631$	−23.1740			−0.922543			−0.461272	+	0.887259i	$0.652607\pi$
$632$	−79.2817	−	79.2817i	−3.15365	−	3.15365i
$633$	−33.1277	+	22.1650i	−1.31671	+	0.880979i
$634$		−	19.6589i		−	0.780756i
$635$	45.7443	−	13.5623i	1.81531	−	0.538204i
$636$	36.4202	+	7.22090i	1.44415	+	0.286327i
$637$	21.5085	−	21.5085i	0.852198	−	0.852198i
$638$	−6.58191	+	6.58191i	−0.260580	+	0.260580i
$639$	40.5805	+	16.7499i	1.60534	+	0.662617i
$640$	83.5007	−	24.7563i	3.30065	−	0.978581i
$641$			25.6636i			1.01365i	0.862049	+	0.506825i	$0.169181\pi$
$641$			25.6636i			1.01365i	−0.862049	+	0.506825i	$0.830819\pi$
$642$	31.7108	+	47.3948i	1.25153	+	1.87052i
$643$	8.93412	+	8.93412i	0.352327	+	0.352327i	0.860975	−	0.508648i	$-0.169854\pi$
$643$	8.93412	+	8.93412i	0.352327	+	0.352327i	−0.508648	+	0.860975i	$0.669854\pi$
$644$	27.6541			1.08972
$645$	4.21221	+	3.49708i	0.165856	+	0.137698i
$646$	12.4156			0.488485
$647$	−19.4396	−	19.4396i	−0.764250	−	0.764250i	0.212838	−	0.977088i	$-0.431729\pi$
$647$	−19.4396	−	19.4396i	−0.764250	−	0.764250i	−0.977088	+	0.212838i	$0.931729\pi$
$648$	−85.5934	+	0.212678i	−3.36243	+	0.00835478i
$649$			1.00192i			0.0393289i
$650$	−78.1664	+	50.8165i	−3.06594	+	1.99319i
$651$	−0.536764	+	2.70728i	−0.0210374	+	0.106107i
$652$	62.9209	−	62.9209i	2.46417	−	2.46417i
$653$	−18.1468	+	18.1468i	−0.710138	+	0.710138i	−0.966564	−	0.256426i	$-0.917455\pi$
$653$	−18.1468	+	18.1468i	−0.710138	+	0.710138i	0.256426	+	0.966564i	$0.417455\pi$
$654$	−11.3162	+	57.0755i	−0.442497	+	2.23183i
$655$	−1.51476	+	2.79148i	−0.0591867	+	0.109072i
$656$		−	82.6748i		−	3.22791i
$657$	23.4877	−	9.76312i	0.916342	−	0.380896i
$658$	23.0200	+	23.0200i	0.897414	+	0.897414i
$659$	−14.6325			−0.570001			−0.285001	−	0.958527i	$-0.591994\pi$
$659$	−14.6325			−0.570001			−0.285001	+	0.958527i	$0.591994\pi$
$660$	−14.8806	+	1.38035i	−0.579228	+	0.0537300i
$661$	−18.4216			−0.716516			−0.358258	−	0.933623i	$-0.616629\pi$
$661$	−18.4216			−0.716516			−0.358258	+	0.933623i	$0.616629\pi$
$662$	49.9412	+	49.9412i	1.94102	+	1.94102i
$663$	17.0723	+	25.5162i	0.663033	+	0.990966i
$664$			113.358i			4.39916i
$665$	−1.76901	−	5.96671i	−0.0685994	−	0.231379i
$666$	27.6433	−	66.9722i	1.07116	−	2.59512i
$667$	−10.8253	+	10.8253i	−0.419158	+	0.419158i
$668$	41.3244	−	41.3244i	1.59889	−	1.59889i
$669$	23.8745	+	4.73352i	0.923042	+	0.183008i
$670$	−52.2682	−	28.3627i	−2.01930	−	1.09575i
$671$			3.44073i			0.132828i
$672$	−50.7809	+	33.9764i	−1.95892	+	1.31067i
$673$	−21.6700	−	21.6700i	−0.835316	−	0.835316i	0.152922	−	0.988238i	$-0.451132\pi$
$673$	−21.6700	−	21.6700i	−0.835316	−	0.835316i	−0.988238	+	0.152922i	$0.951132\pi$
$674$	43.5074			1.67584
$675$	−18.5673	+	18.1729i	−0.714657	+	0.699475i
$676$	−183.487			−7.05720
$677$	−6.96192	−	6.96192i	−0.267568	−	0.267568i	0.560551	−	0.828120i	$-0.310589\pi$
$677$	−6.96192	−	6.96192i	−0.267568	−	0.267568i	−0.828120	+	0.560551i	$0.810589\pi$
$678$	3.01589	−	2.01786i	0.115824	−	0.0774955i
$679$		−	0.0561593i		−	0.00215520i
$680$	−48.5871	−	26.3652i	−1.86323	−	1.01106i
$681$	−3.63217	−	0.720138i	−0.139185	−	0.0275957i
$682$	1.36207	−	1.36207i	0.0521564	−	0.0521564i
$683$	31.6521	−	31.6521i	1.21114	−	1.21114i	0.240482	−	0.970654i	$-0.422695\pi$
$683$	31.6521	−	31.6521i	1.21114	−	1.21114i	0.970654	−	0.240482i	$-0.0773055\pi$
$684$	−10.9513	+	26.5319i	−0.418733	+	1.01447i
$685$	−2.54333	−	8.57840i	−0.0971757	−	0.327764i
$686$		−	49.9402i		−	1.90672i
$687$	−7.93521	−	11.8599i	−0.302747	−	0.452484i
$688$	−15.0442	−	15.0442i	−0.573554	−	0.573554i
$689$	26.6841			1.01658
$690$	−33.4101	+	3.09916i	−1.27190	+	0.117983i
$691$	−43.8725			−1.66899			−0.834494	−	0.551018i	$-0.814240\pi$
$691$	−43.8725			−1.66899			−0.834494	+	0.551018i	$0.814240\pi$
$692$	−16.1742	−	16.1742i	−0.614850	−	0.614850i
$693$	3.10946	−	1.29251i	0.118119	−	0.0490983i
$694$		−	17.3374i		−	0.658119i
$695$	−9.45893	+	17.4314i	−0.358798	+	0.661210i
$696$	15.4806	−	78.0799i	0.586792	−	2.95961i
$697$	−10.0965	+	10.0965i	−0.382430	+	0.382430i
$698$	60.5568	−	60.5568i	2.29211	−	2.29211i
$699$	0.882427	−	4.45071i	0.0333765	−	0.168341i
$700$	−9.05314	+	42.6948i	−0.342176	+	1.61371i
$701$		−	27.8916i		−	1.05345i	−0.850036	−	0.526725i	$-0.823420\pi$
$701$		−	27.8916i		−	1.05345i	0.850036	−	0.526725i	$-0.176580\pi$
$702$	−94.9929	+	19.0794i	−3.58528	+	0.720104i
$703$	−10.9076	−	10.9076i	−0.411389	−	0.411389i
$704$	21.4382			0.807983
$705$	−22.2629	−	18.4833i	−0.838470	−	0.696120i
$706$	29.9500			1.12718
$707$	−11.1322	−	11.1322i	−0.418669	−	0.418669i
$708$	−7.50448	−	11.2162i	−0.282036	−	0.421529i
$709$		−	48.4320i		−	1.81890i	−0.415813	−	0.909450i	$-0.636503\pi$
$709$		−	48.4320i		−	1.81890i	0.415813	−	0.909450i	$-0.363497\pi$
$710$	−85.7899	+	25.4350i	−3.21964	+	0.954560i
$711$	−32.6925	−	13.4941i	−1.22606	−	0.506069i
$712$	−80.8811	+	80.8811i	−3.03115	+	3.03115i
$713$	2.24021	−	2.24021i	0.0838965	−	0.0838965i
$714$	19.2443	+	3.81550i	0.720200	+	0.142792i
$715$	−10.2974	+	3.05297i	−0.385099	+	0.114175i
$716$			58.7910i			2.19712i
$717$	−10.5444	+	7.05505i	−0.393789	+	0.263476i
$718$	−13.5610	−	13.5610i	−0.506093	−	0.506093i
$719$	18.5941			0.693441			0.346721	−	0.937968i	$-0.387295\pi$
$719$	18.5941			0.693441			0.346721	+	0.937968i	$0.387295\pi$
$720$	78.3708	−	63.6567i	2.92071	−	2.37235i
$721$	−6.80698			−0.253505
$722$	−30.8401	−	30.8401i	−1.14775	−	1.14775i
$723$	28.4158	−	19.0124i	1.05680	−	0.707079i
$724$			22.0208i			0.818396i
$725$	−13.1692	−	20.2570i	−0.489091	−	0.752325i
$726$	48.8004	+	9.67549i	1.81115	+	0.359091i
$727$	7.52952	−	7.52952i	0.279254	−	0.279254i	−0.553557	−	0.832811i	$-0.686730\pi$
$727$	7.52952	−	7.52952i	0.279254	−	0.279254i	0.832811	+	0.553557i	$0.186730\pi$
$728$	−73.0699	+	73.0699i	−2.70815	+	2.70815i
$729$	−24.9061	+	10.4254i	−0.922447	+	0.386124i
$730$	−24.7268	+	45.5677i	−0.915178	+	1.68654i
$731$			3.67447i			0.135905i
$732$	−25.7714	−	38.5178i	−0.952537	−	1.42366i
$733$	25.9926	+	25.9926i	0.960058	+	0.960058i	0.999232	−	0.0391744i	$-0.0124728\pi$
$733$	25.9926	+	25.9926i	0.960058	+	0.960058i	−0.0391744	+	0.999232i	$0.512473\pi$
$734$	27.4881			1.01460
$735$	1.59576	+	17.2029i	0.0588606	+	0.634538i
$736$	70.1346			2.58520
$737$	−4.84417	−	4.84417i	−0.178437	−	0.178437i
$738$	−17.2963	−	41.6107i	−0.636686	−	1.53171i
$739$			23.0919i			0.849449i	0.905323	+	0.424724i	$0.139629\pi$
$739$			23.0919i			0.849449i	−0.905323	+	0.424724i	$0.860371\pi$
$740$	30.7499	+	103.716i	1.13039	+	3.81268i
$741$	−4.01186	+	20.2347i	−0.147379	+	0.743339i
$742$	12.0576	−	12.0576i	0.442650	−	0.442650i
$743$	21.8621	−	21.8621i	0.802041	−	0.802041i	−0.181373	−	0.983414i	$-0.558054\pi$
$743$	21.8621	−	21.8621i	0.802041	−	0.802041i	0.983414	+	0.181373i	$0.0580542\pi$
$744$	−3.20359	+	16.1580i	−0.117449	+	0.592381i
$745$	5.52237	+	2.99665i	0.202324	+	0.109789i
$746$		−	48.2063i		−	1.76496i
$747$	13.7251	+	33.0192i	0.502175	+	1.20811i
$748$	−7.09254	−	7.09254i	−0.259329	−	0.259329i
$749$	19.1850			0.701004
$750$	6.15271	−	52.5960i	0.224665	−	1.92053i
$751$	29.6285			1.08116			0.540580	−	0.841292i	$-0.318205\pi$
$751$	29.6285			1.08116			0.540580	+	0.841292i	$0.318205\pi$
$752$	79.5136	+	79.5136i	2.89956	+	2.89956i
$753$	17.9925	+	26.8916i	0.655685	+	0.979983i
$754$		−	90.1050i		−	3.28143i
$755$	−8.12834	−	4.41074i	−0.295820	−	0.160523i
$756$	−25.1283	+	37.7593i	−0.913907	+	1.37329i
$757$	−25.9551	+	25.9551i	−0.943354	+	0.943354i	−0.998479	−	0.0551252i	$-0.982444\pi$
$757$	−25.9551	+	25.9551i	−0.943354	+	0.943354i	0.0551252	+	0.998479i	$0.482444\pi$
$758$	−44.1680	+	44.1680i	−1.60425	+	1.60425i
$759$	−3.79156	−	0.751741i	−0.137625	−	0.0272865i
$760$	−10.5581	−	35.6114i	−0.382982	−	1.29176i
$761$			6.25906i			0.226891i	0.993544	+	0.113445i	$0.0361887\pi$
$761$			6.25906i			0.226891i	−0.993544	+	0.113445i	$0.963811\pi$
$762$	−83.9966	+	56.2002i	−3.04287	+	2.03592i
$763$	13.8422	+	13.8422i	0.501120	+	0.501120i
$764$	101.348			3.66664
$765$	−17.3448	−	1.79692i	−0.627101	−	0.0649676i
$766$	16.3767			0.591714
$767$	−6.85806	−	6.85806i	−0.247630	−	0.247630i
$768$	−65.7025	+	43.9601i	−2.37084	+	1.58627i
$769$		−	12.0496i		−	0.434519i	−0.976114	−	0.217259i	$-0.930288\pi$
$769$		−	12.0496i		−	0.434519i	0.976114	−	0.217259i	$-0.0697117\pi$
$770$	−3.27349	+	6.03256i	−0.117969	+	0.217398i
$771$	−25.2261	−	5.00150i	−0.908497	−	0.180125i
$772$	−25.0300	+	25.0300i	−0.900851	+	0.900851i
$773$	29.0226	−	29.0226i	1.04387	−	1.04387i	0.0448789	−	0.998992i	$-0.485710\pi$
$773$	29.0226	−	29.0226i	1.04387	−	1.04387i	0.998992	−	0.0448789i	$-0.0142902\pi$
$774$	−10.7192	−	4.42444i	−0.385294	−	0.159033i
$775$	2.72526	+	4.19201i	0.0978941	+	0.150582i
$776$		−	0.335178i		−	0.0120322i
$777$	−13.5548	−	20.2590i	−0.486277	−	0.726788i
$778$	71.2039	+	71.2039i	2.55278	+	2.55278i
$779$	−9.59407			−0.343743
$780$	92.4082	−	111.305i	3.30874	−	3.98536i
$781$	−10.3082			−0.368857
$782$	−15.9242	−	15.9242i	−0.569448	−	0.569448i
$783$	−4.94445	−	24.6176i	−0.176700	−	0.879761i
$784$		−	67.1407i		−	2.39788i
$785$	−0.110942	+	0.0328921i	−0.00395968	+	0.00117397i
$786$	1.30834	−	6.59887i	0.0466668	−	0.235374i
$787$	3.08781	−	3.08781i	0.110069	−	0.110069i	−0.649928	−	0.759996i	$-0.725201\pi$
$787$	3.08781	−	3.08781i	0.110069	−	0.110069i	0.759996	+	0.649928i	$0.225201\pi$
$788$	−27.5066	+	27.5066i	−0.979883	+	0.979883i
$789$	−0.972558	+	4.90530i	−0.0346240	+	0.174633i
$790$	69.1142	−	20.4910i	2.45897	−	0.729038i
$791$		−	1.22080i		−	0.0434067i
$792$	18.5583	−	7.71413i	0.659441	−	0.274110i
$793$	−23.5515	−	23.5515i	−0.836337	−	0.836337i
$794$	−7.05155			−0.250250
$795$	−9.68133	+	11.6611i	−0.343361	+	0.413576i
$796$	17.2673			0.612023
$797$	−8.82182	−	8.82182i	−0.312485	−	0.312485i	0.533387	−	0.845872i	$-0.320919\pi$
$797$	−8.82182	−	8.82182i	−0.312485	−	0.312485i	−0.845872	+	0.533387i	$0.820919\pi$
$798$	7.33054	+	10.9562i	0.259498	+	0.387845i
$799$		−	19.4208i		−	0.687058i
$800$	−22.9600	+	108.280i	−0.811760	+	3.82828i
$801$	−13.7664	+	33.3521i	−0.486410	+	1.17844i
$802$	26.9259	−	26.9259i	0.950786	−	0.950786i
$803$	−4.22318	+	4.22318i	−0.149033	+	0.149033i
$804$	90.5120	+	17.9455i	3.19211	+	0.632889i
$805$	−5.38394	+	9.92180i	−0.189759	+	0.349698i
$806$			18.6465i			0.656795i
$807$	10.6932	−	7.15458i	0.376418	−	0.251853i
$808$	−66.4407	−	66.4407i	−2.33738	−	2.33738i
$809$	−21.9850			−0.772950			−0.386475	−	0.922300i	$-0.626307\pi$
$809$	−21.9850			−0.772950			−0.386475	+	0.922300i	$0.626307\pi$
$810$	26.1269	−	48.4346i	0.918005	−	1.70182i
$811$	14.1952			0.498461			0.249230	−	0.968444i	$-0.419822\pi$
$811$	14.1952			0.498461			0.249230	+	0.968444i	$0.419822\pi$
$812$	−29.8258	−	29.8258i	−1.04668	−	1.04668i
$813$	12.9619	−	8.67251i	0.454594	−	0.304158i
$814$			17.0122i			0.596278i
$815$	10.3249	+	34.8249i	0.361666	+	1.21986i
$816$	66.4718	+	13.1792i	2.32698	+	0.461363i
$817$	−1.74582	+	1.74582i	−0.0610784	+	0.0610784i
$818$	38.9976	−	38.9976i	1.36352	−	1.36352i
$819$	−12.4368	+	30.1310i	−0.434578	+	1.05286i
$820$	59.1364	+	32.0896i	2.06513	+	1.12062i
$821$			29.1708i			1.01807i	0.860746	+	0.509034i	$0.169997\pi$
$821$			29.1708i			1.01807i	−0.860746	+	0.509034i	$0.830003\pi$
$822$	10.5392	+	15.7518i	0.367597	+	0.549408i
$823$	16.4285	+	16.4285i	0.572662	+	0.572662i	0.932871	−	0.360210i	$-0.117295\pi$
$823$	16.4285	+	16.4285i	0.572662	+	0.572662i	−0.360210	+	0.932871i	$0.617295\pi$
$824$	−40.6264			−1.41529
$825$	2.40185	−	5.60766i	0.0836217	−	0.195234i
$826$	−6.19785			−0.215651
$827$	19.1727	+	19.1727i	0.666699	+	0.666699i	0.956950	−	0.290252i	$-0.0937391\pi$
$827$	19.1727	+	19.1727i	0.666699	+	0.666699i	−0.290252	+	0.956950i	$0.593739\pi$
$828$	48.0758	−	19.9837i	1.67075	−	0.694480i
$829$			6.17333i			0.214409i	0.994237	+	0.107204i	$0.0341899\pi$
$829$			6.17333i			0.214409i	−0.994237	+	0.107204i	$0.965810\pi$
$830$	−64.0596	−	34.7611i	−2.22354	−	1.20658i
$831$	2.08305	−	10.5063i	0.0722600	−	0.364459i
$832$	−146.742	+	146.742i	−5.08738	+	5.08738i
$833$	−8.19939	+	8.19939i	−0.284092	+	0.284092i
$834$	8.16990	−	41.2066i	0.282901	−	1.42687i
$835$	6.78107	+	22.8719i	0.234669	+	0.791514i
$836$		−	6.73963i		−	0.233095i
$837$	1.02321	+	5.09441i	0.0353675	+	0.176089i
$838$	−11.2958	−	11.2958i	−0.390207	−	0.390207i
$839$	42.1371			1.45474			0.727368	−	0.686248i	$-0.240743\pi$
$839$	42.1371			1.45474			0.727368	+	0.686248i	$0.240743\pi$
$840$	−5.42122	−	58.4426i	−0.187050	−	2.01646i
$841$	−5.64912			−0.194797
$842$	8.96338	+	8.96338i	0.308899	+	0.308899i
$843$	−29.6574	−	44.3258i	−1.02145	−	1.52666i
$844$			126.059i			4.33913i
$845$	35.7229	−	65.8320i	1.22891	−	2.26469i
$846$	56.6546	+	23.3847i	1.94782	+	0.803982i
$847$	11.8352	−	11.8352i	0.406664	−	0.406664i
$848$	41.6484	−	41.6484i	1.43021	−	1.43021i
$849$	28.9089	+	5.73168i	0.992152	+	0.196711i
$850$	29.7983	−	19.3721i	1.02207	−	0.664456i
$851$			27.9801i			0.959147i
$852$	115.397	−	77.2094i	3.95343	−	2.64515i
$853$	−0.537052	−	0.537052i	−0.0183883	−	0.0183883i	0.697853	−	0.716241i	$-0.254139\pi$
$853$	−0.537052	−	0.537052i	−0.0183883	−	0.0183883i	−0.716241	+	0.697853i	$0.754139\pi$
$854$	−21.2842			−0.728331
$855$	−7.38710	−	9.09461i	−0.252634	−	0.311029i
$856$	114.503			3.91362
$857$	−21.3288	−	21.3288i	−0.728579	−	0.728579i	0.241758	−	0.970337i	$-0.422276\pi$
$857$	−21.3288	−	21.3288i	−0.728579	−	0.728579i	−0.970337	+	0.241758i	$0.922276\pi$
$858$	18.9082	−	12.6511i	0.645516	−	0.431900i
$859$		−	6.51296i		−	0.222219i	−0.993808	−	0.111110i	$-0.964560\pi$
$859$		−	6.51296i		−	0.222219i	0.993808	−	0.111110i	$-0.0354405\pi$
$860$	16.6003	−	4.92166i	0.566064	−	0.167827i
$861$	−14.8709	−	2.94840i	−0.506799	−	0.100481i
$862$	43.0419	−	43.0419i	1.46601	−	1.46601i
$863$	−35.2927	+	35.2927i	−1.20138	+	1.20138i	−0.227631	+	0.973747i	$0.573098\pi$
$863$	−35.2927	+	35.2927i	−1.20138	+	1.20138i	−0.973747	+	0.227631i	$0.926902\pi$
$864$	−63.7288	+	95.7628i	−2.16810	+	3.25792i
$865$	8.95194	−	2.65408i	0.304375	−	0.0902414i
$866$			39.8852i			1.35536i
$867$	9.86566	+	14.7452i	0.335055	+	0.500772i
$868$	6.17221	+	6.17221i	0.209498	+	0.209498i
$869$	8.30453			0.281712
$870$	39.3764	+	32.6913i	1.33498	+	1.10834i
$871$	66.3157			2.24702
$872$	82.6147	+	82.6147i	2.79769	+	2.79769i
$873$	−0.0405824	−	0.0976313i	−0.00137351	−	0.00330432i
$874$		−	15.1318i		−	0.511841i
$875$	−13.5556	−	11.5603i	−0.458263	−	0.390810i
$876$	15.6450	−	78.9089i	0.528596	−	2.66608i
$877$	16.5377	−	16.5377i	0.558438	−	0.558438i	−0.370425	−	0.928863i	$-0.620788\pi$
$877$	16.5377	−	16.5377i	0.558438	−	0.558438i	0.928863	+	0.370425i	$0.120788\pi$
$878$	−35.5151	+	35.5151i	−1.19858	+	1.19858i
$879$	7.24642	−	36.5489i	0.244416	−	1.23276i
$880$	−11.3070	+	20.8371i	−0.381159	+	0.702419i
$881$		−	0.468258i		−	0.0157760i	−0.999969	−	0.00788800i	$-0.997489\pi$
$881$		−	0.468258i		−	0.0157760i	0.999969	−	0.00788800i	$-0.00251085\pi$
$882$	−14.0464	−	33.7923i	−0.472968	−	1.13784i
$883$	−1.46417	−	1.46417i	−0.0492734	−	0.0492734i	0.682041	−	0.731314i	$-0.261093\pi$
$883$	−1.46417	−	1.46417i	−0.0492734	−	0.0492734i	−0.731314	+	0.682041i	$0.761093\pi$
$884$	97.0955			3.26568
$885$	5.48520	−	0.508815i	0.184383	−	0.0171036i
$886$	−54.4991			−1.83093
$887$	1.09095	+	1.09095i	0.0366304	+	0.0366304i	0.725185	−	0.688554i	$-0.241754\pi$
$887$	1.09095	+	1.09095i	0.0366304	+	0.0366304i	−0.688554	+	0.725185i	$0.741754\pi$
$888$	−80.9000	−	120.913i	−2.71483	−	4.05757i
$889$			34.0010i			1.14036i
$890$	−20.9044	−	70.5086i	−0.700718	−	2.36345i
$891$	4.47170	−	4.49397i	0.149807	−	0.150554i
$892$	54.4304	−	54.4304i	1.82246	−	1.82246i
$893$	9.22722	−	9.22722i	0.308777	−	0.308777i
$894$	−13.0545	−	2.58828i	−0.436608	−	0.0865649i
$895$	−21.0932	−	11.4460i	−0.705068	−	0.382596i
$896$			62.0648i			2.07344i
$897$	31.0985	−	20.8073i	1.03835	−	0.694735i
$898$	21.6470	+	21.6470i	0.722370	+	0.722370i
$899$	−4.83228			−0.161165
$900$	15.1139	+	80.7658i	0.503798	+	2.69219i
$901$	−10.1724			−0.338892
$902$	7.48176	+	7.48176i	0.249115	+	0.249115i
$903$	−3.24255	+	2.16952i	−0.107905	+	0.0721970i
$904$		−	7.28617i		−	0.242334i
$905$	−7.90067	−	4.28720i	−0.262627	−	0.142511i
$906$	19.2148	+	3.80966i	0.638370	+	0.126568i
$907$	−11.6212	+	11.6212i	−0.385876	+	0.385876i	−0.873214	−	0.487338i	$-0.837968\pi$
$907$	−11.6212	+	11.6212i	−0.385876	+	0.385876i	0.487338	+	0.873214i	$0.337968\pi$
$908$	−8.28081	+	8.28081i	−0.274808	+	0.274808i
$909$	−27.3974	−	11.3085i	−0.908715	−	0.375080i
$910$	−18.8855	−	63.6990i	−0.626050	−	2.11160i
$911$			6.71279i			0.222405i	0.993798	+	0.111202i	$0.0354702\pi$
$911$			6.71279i			0.222405i	−0.993798	+	0.111202i	$0.964530\pi$
$912$	25.3205	+	37.8438i	0.838444	+	1.25313i
$913$	−5.93698	−	5.93698i	−0.196486	−	0.196486i
$914$	−82.4318			−2.72660
$915$	18.8369	−	1.74734i	0.622729	−	0.0577652i
$916$	−45.1300			−1.49114
$917$	−1.60038	−	1.60038i	−0.0528493	−	0.0528493i
$918$	36.2128	−	7.27336i	1.19520	−	0.240057i
$919$			17.4804i			0.576624i	0.957537	+	0.288312i	$0.0930940\pi$
$919$			17.4804i			0.576624i	−0.957537	+	0.288312i	$0.906906\pi$
$920$	−32.1332	+	59.2167i	−1.05940	+	1.95232i
$921$	−2.89282	+	14.5905i	−0.0953216	+	0.480775i
$922$	−65.1596	+	65.1596i	−2.14592	+	2.14592i
$923$	70.5588	−	70.5588i	2.32247	−	2.32247i
$924$	2.07119	−	10.4465i	0.0681372	−	0.343664i
$925$	−43.1982	−	9.15988i	−1.42035	−	0.301175i
$926$		−	35.8699i		−	1.17876i
$927$	−11.8337	+	4.91892i	−0.388671	+	0.161559i
$928$	−75.6424	−	75.6424i	−2.48308	−	2.48308i
$929$	20.7835			0.681884			0.340942	−	0.940084i	$-0.389254\pi$
$929$	20.7835			0.681884			0.340942	+	0.940084i	$0.389254\pi$
$930$	−8.14862	−	6.76519i	−0.267204	−	0.221839i
$931$	−7.79140			−0.255353
$932$	−10.1470	−	10.1470i	−0.332375	−	0.332375i
$933$	−4.45766	−	6.66240i	−0.145937	−	0.218117i
$934$		−	70.5780i		−	2.30938i
$935$	3.92552	−	1.16384i	0.128378	−	0.0380617i
$936$	−74.2274	+	179.832i	−2.42620	+	5.87800i
$937$	15.0275	−	15.0275i	0.490927	−	0.490927i	−0.417671	−	0.908598i	$-0.637153\pi$
$937$	15.0275	−	15.0275i	0.490927	−	0.490927i	0.908598	+	0.417671i	$0.137153\pi$
$938$	29.9659	−	29.9659i	0.978420	−	0.978420i
$939$	33.4185	+	6.62577i	1.09057	+	0.216224i
$940$	−87.7379	+	26.0126i	−2.86170	+	0.848438i
$941$		−	3.71889i		−	0.121232i	−0.998161	−	0.0606162i	$-0.980693\pi$
$941$		−	3.71889i		−	0.121232i	0.998161	−	0.0606162i	$-0.0193066\pi$
$942$	0.203714	−	0.136300i	0.00663735	−	0.00444090i
$943$	12.3053	+	12.3053i	0.400716	+	0.400716i
$944$	−21.4080			−0.696772
$945$	−8.65517	−	16.3669i	−0.281553	−	0.532415i
$946$	2.72288			0.0885286
$947$	15.3124	+	15.3124i	0.497586	+	0.497586i	0.910686	−	0.413100i	$-0.135554\pi$
$947$	15.3124	+	15.3124i	0.497586	+	0.497586i	−0.413100	+	0.910686i	$0.635554\pi$
$948$	−92.9662	+	62.2016i	−3.01940	+	2.02021i
$949$		−	57.8144i		−	1.87674i
$950$	23.3619	+	4.95372i	0.757959	+	0.160720i
$951$	−12.2141	−	2.42164i	−0.396068	−	0.0785270i
$952$	27.8554	−	27.8554i	0.902800	−	0.902800i
$953$	23.4013	−	23.4013i	0.758043	−	0.758043i	−0.217923	−	0.975966i	$-0.569928\pi$
$953$	23.4013	−	23.4013i	0.758043	−	0.758043i	0.975966	+	0.217923i	$0.0699281\pi$
$954$	12.2486	−	29.6751i	0.396564	−	0.960765i
$955$	−19.7313	+	36.3619i	−0.638491	+	1.17664i
$956$			40.1243i			1.29771i
$957$	3.27855	+	4.90010i	0.105980	+	0.158398i
$958$	62.6588	+	62.6588i	2.02442	+	2.02442i
$959$	6.37619			0.205898
$960$	−10.8872	−	117.367i	−0.351381	−	3.78801i
$961$	1.00000			0.0322581
$962$	−116.447	−	116.447i	−3.75440	−	3.75440i
$963$	33.3525	−	13.8636i	1.07477	−	0.446749i
$964$		−	108.129i		−	3.48261i
$965$	−4.10727	−	13.8534i	−0.132218	−	0.445957i
$966$	4.65024	−	23.4545i	0.149619	−	0.754635i
$967$	13.5129	−	13.5129i	0.434545	−	0.434545i	−0.455626	−	0.890171i	$-0.650585\pi$
$967$	13.5129	−	13.5129i	0.434545	−	0.434545i	0.890171	+	0.455626i	$0.150585\pi$
$968$	70.6368	−	70.6368i	2.27035	−	2.27035i
$969$	1.52939	−	7.71378i	0.0491310	−	0.247802i
$970$	0.189411	+	0.102782i	0.00608163	+	0.00330012i
$971$		−	37.4937i		−	1.20323i	−0.798787	−	0.601614i	$-0.794524\pi$
$971$		−	37.4937i		−	1.20323i	0.798787	−	0.601614i	$-0.205476\pi$
$972$	−16.3988	+	83.8018i	−0.525992	+	2.68794i
$973$	−9.99358	−	9.99358i	−0.320379	−	0.320379i
$974$	39.2924			1.25901
$975$	21.9434	+	54.8243i	0.702752	+	1.75578i
$976$	−73.5180			−2.35325
$977$	−6.09991	−	6.09991i	−0.195153	−	0.195153i	0.602765	−	0.797919i	$-0.294066\pi$
$977$	−6.09991	−	6.09991i	−0.195153	−	0.195153i	−0.797919	+	0.602765i	$0.794066\pi$
$978$	−42.7850	−	63.9462i	−1.36811	−	2.04477i
$979$		−	8.47207i		−	0.270769i
$980$	48.0250	+	26.0602i	1.53410	+	0.832462i
$981$	34.0669	+	14.0614i	1.08767	+	0.448947i
$982$	1.07280	−	1.07280i	0.0342346	−	0.0342346i
$983$	−19.8321	+	19.8321i	−0.632546	+	0.632546i	−0.948706	−	0.316160i	$-0.897606\pi$
$983$	−19.8321	+	19.8321i	−0.632546	+	0.632546i	0.316160	+	0.948706i	$0.397606\pi$
$984$	−88.7546	−	17.5971i	−2.82939	−	0.560974i
$985$	−4.51366	−	15.2241i	−0.143817	−	0.485081i
$986$			34.3495i			1.09391i
$987$	17.1379	−	11.4666i	0.545507	−	0.364986i
$988$	46.1321	+	46.1321i	1.46766	+	1.46766i
$989$	4.47835			0.142403
$990$	−1.33157	+	12.8530i	−0.0423199	+	0.408494i
$991$	−10.9125			−0.346647			−0.173323	−	0.984865i	$-0.555451\pi$
$991$	−10.9125			−0.346647			−0.173323	+	0.984865i	$0.555451\pi$
$992$	15.6536	+	15.6536i	0.497002	+	0.497002i
$993$	37.1802	−	24.8765i	1.17988	−	0.789431i
$994$		−	63.7663i		−	2.02254i
$995$	−3.36175	+	6.19520i	−0.106575	+	0.196401i
$996$	110.931	+	21.9939i	3.51498	+	0.696904i
$997$	−7.81551	+	7.81551i	−0.247520	+	0.247520i	−0.819952	−	0.572432i	$-0.806000\pi$
$997$	−7.81551	+	7.81551i	−0.247520	+	0.247520i	0.572432	+	0.819952i	$0.306000\pi$
$998$	−14.9266	+	14.9266i	−0.472492	+	0.472492i
$999$	−38.2045	−	25.4246i	−1.20874	−	0.804397i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	465.2.k.a.218.2	yes	60
3.2	odd	2	inner	465.2.k.a.218.29	yes	60
5.2	odd	4	inner	465.2.k.a.32.29	yes	60
15.2	even	4	inner	465.2.k.a.32.2	✓	60

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
465.2.k.a.32.2	✓	60	15.2	even	4	inner
465.2.k.a.32.29	yes	60	5.2	odd	4	inner
465.2.k.a.218.2	yes	60	1.1	even	1	trivial
465.2.k.a.218.29	yes	60	3.2	odd	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 465 = 3 \cdot 5 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	465.k (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.93363 - 1.93363i) q^{2} +(-1.43955 + 0.963170i) q^{3} +5.47785i q^{4} +(-1.96536 - 1.06648i) q^{5} +(4.64597 + 0.921141i) q^{6} +(1.12676 - 1.12676i) q^{7} +(6.72487 - 6.72487i) q^{8} +(1.14461 - 2.77306i) q^{9} +(1.73810 + 5.86244i) q^{10} +0.704412i q^{11} +(-5.27610 - 7.88564i) q^{12} +(-4.82163 - 4.82163i) q^{13} -4.35746 q^{14} +(3.85643 - 0.357727i) q^{15} -15.0511 q^{16} +(1.83808 + 1.83808i) q^{17} +(-7.57532 + 3.14883i) q^{18} +1.74662i q^{19} +(5.84200 - 10.7659i) q^{20} +(-0.536764 + 2.70728i) q^{21} +(1.36207 - 1.36207i) q^{22} +(2.24021 - 2.24021i) q^{23} +(-3.20359 + 16.1580i) q^{24} +(2.72526 + 4.19201i) q^{25} +18.6465i q^{26} +(1.02321 + 5.09441i) q^{27} +(6.17221 + 6.17221i) q^{28} -4.83228 q^{29} +(-8.14862 - 6.76519i) q^{30} +1.00000 q^{31} +(15.6536 + 15.6536i) q^{32} +(-0.678468 - 1.01404i) q^{33} -7.10835i q^{34} +(-3.41614 + 1.01282i) q^{35} +(15.1904 + 6.26998i) q^{36} +(-6.24498 + 6.24498i) q^{37} +(3.37732 - 3.37732i) q^{38} +(11.5850 + 2.29692i) q^{39} +(-20.3887 + 6.04486i) q^{40} +5.49292i q^{41} +(6.27278 - 4.19698i) q^{42} +(0.999538 + 0.999538i) q^{43} -3.85866 q^{44} +(-5.20697 + 4.22936i) q^{45} -8.66347 q^{46} +(-5.28289 - 5.28289i) q^{47} +(21.6669 - 14.4968i) q^{48} +4.46084i q^{49} +(2.83617 - 13.3754i) q^{50} +(-4.41640 - 0.875625i) q^{51} +(26.4122 - 26.4122i) q^{52} +(-2.76712 + 2.76712i) q^{53} +(7.87219 - 11.8292i) q^{54} +(0.751239 - 1.38442i) q^{55} -15.1546i q^{56} +(-1.68230 - 2.51435i) q^{57} +(9.34383 + 9.34383i) q^{58} +1.42235 q^{59} +(1.95958 + 21.1249i) q^{60} +4.88455 q^{61} +(-1.93363 - 1.93363i) q^{62} +(-1.83488 - 4.41426i) q^{63} -30.4342i q^{64} +(4.33407 + 14.6184i) q^{65} +(-0.648863 + 3.27268i) q^{66} +(-6.87690 + 6.87690i) q^{67} +(-10.0687 + 10.0687i) q^{68} +(-1.06719 + 5.38260i) q^{69} +(8.56397 + 4.64713i) q^{70} +14.6338i q^{71} +(-10.9512 - 26.3458i) q^{72} +(5.99532 + 5.99532i) q^{73} +24.1510 q^{74} +(-7.96076 - 3.40973i) q^{75} -9.56774 q^{76} +(0.793701 + 0.793701i) q^{77} +(-17.9597 - 26.8425i) q^{78} -11.7893i q^{79} +(29.5809 + 16.0517i) q^{80} +(-6.37975 - 6.34813i) q^{81} +(10.6213 - 10.6213i) q^{82} +(-8.42829 + 8.42829i) q^{83} +(-14.8301 - 2.94031i) q^{84} +(-1.65222 - 5.57276i) q^{85} -3.86547i q^{86} +(6.95630 - 4.65430i) q^{87} +(4.73708 + 4.73708i) q^{88} -12.0272 q^{89} +(18.2464 + 1.89032i) q^{90} -10.8656 q^{91} +(12.2715 + 12.2715i) q^{92} +(-1.43955 + 0.963170i) q^{93} +20.4303i q^{94} +(1.86273 - 3.43274i) q^{95} +(-37.6112 - 7.45704i) q^{96} +(0.0249208 - 0.0249208i) q^{97} +(8.62561 - 8.62561i) q^{98} +(1.95338 + 0.806274i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 60 q - 4 q^{6} - 32 q^{10} + 4 q^{13} + 20 q^{15} - 60 q^{16} - 46 q^{18} - 4 q^{21} + 8 q^{22} - 8 q^{25} - 6 q^{27} + 112 q^{28} + 54 q^{30} + 60 q^{31} - 30 q^{33} - 4 q^{36} - 36 q^{37} - 36 q^{40}+ \cdots - 8 q^{97}+O(q^{100}) \) 60 * q - 4 * q^6 - 32 * q^10 + 4 * q^13 + 20 * q^15 - 60 * q^16 - 46 * q^18 - 4 * q^21 + 8 * q^22 - 8 * q^25 - 6 * q^27 + 112 * q^28 + 54 * q^30 + 60 * q^31 - 30 * q^33 - 4 * q^36 - 36 * q^37 - 36 * q^40 + 44 * q^42 + 16 * q^43 + 14 * q^45 + 40 * q^46 - 104 * q^48 - 48 * q^51 - 12 * q^52 - 48 * q^55 + 42 * q^57 + 80 * q^58 + 60 * q^60 - 8 * q^61 - 10 * q^63 - 24 * q^66 - 88 * q^67 - 84 * q^70 + 84 * q^72 + 60 * q^73 + 14 * q^75 + 72 * q^76 - 152 * q^78 - 132 * q^81 - 60 * q^82 - 16 * q^85 + 34 * q^87 + 124 * q^88 + 190 * q^90 + 64 * q^91 - 88 * q^96 - 8 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more